33:I[196793,["/_next/static/chunks/3bel3_dvibr52.js?dpl=nogit-1790346806","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790346806","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790346806","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790346806","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790346806","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790346806","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790346806","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790346806","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790346806","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790346806","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790346806","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790346806","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790346806","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790346806","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790346806","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790346806","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790346806","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790346806","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790346806","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790346806","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790346806","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790346806","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790346806","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790346806","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790346806","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790346806","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790346806","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790346806","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790346806","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790346806","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790346806","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790346806","/_next/static/chunks/2kd27y977t9dq.js?dpl=nogit-1790346806","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790346806","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790346806","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790346806","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790346806","/_next/static/chunks/1ru1c1qhj59ru.js?dpl=nogit-1790346806","/_next/static/chunks/3pn3stynwpee4.js?dpl=nogit-1790346806","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790346806","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790346806","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790346806","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790346806","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790346806","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790346806","/_next/static/chunks/3xsnraawr9el9.js?dpl=nogit-1790346806","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790346806","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790346806","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790346806","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790346806","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790346806","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790346806","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790346806","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790346806","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790346806","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790346806","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790346806","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790346806","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790346806","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790346806","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790346806","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790346806","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790346806","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790346806","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790346806","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790346806","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790346806"],"Gingerbread"] 35:I[647935,["/_next/static/chunks/3bel3_dvibr52.js?dpl=nogit-1790346806","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790346806","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790346806","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790346806","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790346806","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790346806","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790346806","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790346806","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790346806","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790346806","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790346806","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790346806","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790346806","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790346806","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790346806","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790346806","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790346806","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790346806","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790346806","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790346806","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790346806","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790346806","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790346806","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790346806","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790346806","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790346806","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790346806","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790346806","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790346806","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790346806","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790346806","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790346806","/_next/static/chunks/2kd27y977t9dq.js?dpl=nogit-1790346806","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790346806","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790346806","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790346806","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790346806","/_next/static/chunks/1ru1c1qhj59ru.js?dpl=nogit-1790346806","/_next/static/chunks/3pn3stynwpee4.js?dpl=nogit-1790346806","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790346806","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790346806","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790346806","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790346806","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790346806","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790346806","/_next/static/chunks/3xsnraawr9el9.js?dpl=nogit-1790346806","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790346806","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790346806","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790346806","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790346806","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790346806","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790346806","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790346806","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790346806","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790346806","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790346806","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790346806","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790346806","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790346806","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790346806","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790346806","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790346806","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790346806","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790346806","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790346806","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790346806","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790346806"],"RecordResourceResume"] 36:I[830476,["/_next/static/chunks/3bel3_dvibr52.js?dpl=nogit-1790346806","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790346806","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790346806","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790346806","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790346806","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790346806","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790346806","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790346806","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790346806","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790346806","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790346806","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790346806","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790346806","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790346806","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790346806","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790346806","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790346806","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790346806","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790346806","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790346806","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790346806","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790346806","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790346806","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790346806","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790346806","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790346806","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790346806","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790346806","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790346806","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790346806","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790346806","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790346806","/_next/static/chunks/2kd27y977t9dq.js?dpl=nogit-1790346806","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790346806","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790346806","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790346806","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790346806","/_next/static/chunks/1ru1c1qhj59ru.js?dpl=nogit-1790346806","/_next/static/chunks/3pn3stynwpee4.js?dpl=nogit-1790346806","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790346806","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790346806","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790346806","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790346806","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790346806","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790346806","/_next/static/chunks/3xsnraawr9el9.js?dpl=nogit-1790346806","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790346806","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790346806","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790346806","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790346806","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790346806","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790346806","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790346806","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790346806","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790346806","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790346806","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790346806","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790346806","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790346806","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790346806","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790346806","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790346806","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790346806","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790346806","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790346806","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790346806","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790346806"],"FlashcardAccessBranch"] 37:I[315438,["/_next/static/chunks/3bel3_dvibr52.js?dpl=nogit-1790346806","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790346806","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790346806","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790346806","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790346806","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790346806","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790346806","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790346806","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790346806","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790346806","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790346806","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790346806","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790346806","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790346806","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790346806","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790346806","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790346806","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790346806","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790346806","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790346806","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790346806","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790346806","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790346806","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790346806","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790346806","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790346806","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790346806","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790346806","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790346806","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790346806","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790346806","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790346806","/_next/static/chunks/2kd27y977t9dq.js?dpl=nogit-1790346806","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790346806","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790346806","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790346806","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790346806","/_next/static/chunks/1ru1c1qhj59ru.js?dpl=nogit-1790346806","/_next/static/chunks/3pn3stynwpee4.js?dpl=nogit-1790346806","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790346806","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790346806","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790346806","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790346806","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790346806","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790346806","/_next/static/chunks/3xsnraawr9el9.js?dpl=nogit-1790346806","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790346806","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790346806","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790346806","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790346806","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790346806","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790346806","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790346806","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790346806","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790346806","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790346806","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790346806","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790346806","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790346806","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790346806","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790346806","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790346806","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790346806","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790346806","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790346806","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790346806","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790346806"],"TopicFlashcardRunner"] 24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/igcse/maths/edexcel/grade-5-11-sohcahtoa-trigonometry/flashcards","label":"SOHCAHTOA (Trigonometry)","subjectCode":"igcse_maths","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"5b5e7d96-46db-4e4a-aa04-57b4d417c881","title":"SOHCAHTOA (Trigonometry) Flashcards","topicId":"c3a73f54-72a9-475c-a240-7b9435772505","topicSlug":"grade-5-11-sohcahtoa-trigonometry","cards":[{"id":"05c51ca5-6d77-41d4-abe7-c1e9e933e28e","cardType":"basic","points":1,"front":"Before using SOHCAHTOA, what type of triangle must the diagram contain?","back":"A right-angled triangle.","mcqOptions":[{"text":"A right-angled triangle.","correct":true,"explanation":"SOHCAHTOA defines trigonometric ratios using the opposite, adjacent and hypotenuse sides of a right-angled triangle, which must contain a $90^\\circ$ angle."},{"text":"An acute-angled triangle.","correct":false,"explanation":"An acute-angled triangle has no $90^\\circ$ angle, so the standard SOHCAHTOA side relationships do not apply directly. The diagram must contain a right-angled triangle."},{"text":"An obtuse-angled triangle.","correct":false,"explanation":"An obtuse-angled triangle contains an angle greater than $90^\\circ$, rather than a right angle. Basic SOHCAHTOA requires a right-angled triangle."},{"text":"An equilateral triangle.","correct":false,"explanation":"An equilateral triangle has three $60^\\circ$ angles and therefore no hypotenuse. Basic SOHCAHTOA requires a right-angled triangle."}]},{"id":"fa020e93-67bf-437a-80d7-ac2db17be270","cardType":"basic","points":1,"front":"If a side is opposite the $90^\\circ$ angle, what is its label?","back":"The hypotenuse.","mcqOptions":[{"text":"The hypotenuse.","correct":true,"explanation":"The side directly opposite the $90^\\circ$ angle is always the hypotenuse. It is also the longest side of a right-angled triangle."},{"text":"The opposite.","correct":false,"explanation":"The opposite side is identified relative to the chosen acute angle, not the $90^\\circ$ angle. The side opposite $90^\\circ$ is the hypotenuse."},{"text":"The adjacent.","correct":false,"explanation":"The adjacent side lies beside the chosen acute angle and is not the hypotenuse. The side opposite the $90^\\circ$ angle is the hypotenuse."},{"text":"The base.","correct":false,"explanation":"“Base” may describe a side’s position in a drawing, but it is not the required trigonometric label. The side opposite $90^\\circ$ is the hypotenuse."}]},{"id":"8aeb5e12-ed28-4d30-9029-6cdc32c35567","cardType":"basic","points":1,"front":"From the chosen angle, a side directly across has what label?","back":"The opposite side.","mcqOptions":[{"text":"The opposite side.","correct":true,"explanation":"The side directly across from the chosen acute angle is labelled the opposite side because it does not touch that angle."},{"text":"The adjacent side.","correct":false,"explanation":"The adjacent side touches the chosen angle, whereas the side directly across from that angle is labelled the opposite side."},{"text":"The hypotenuse side.","correct":false,"explanation":"The hypotenuse is specifically the side opposite the $90^\\circ$ angle, not necessarily the side across from the chosen acute angle. That side is opposite."},{"text":"The base side.","correct":false,"explanation":"“Base” describes how a diagram may be drawn rather than the side’s relationship to the chosen angle. The side directly across is the opposite side."}]},{"id":"0b2c283f-cde7-4022-9fc5-a4ef81215cb1","cardType":"basic","points":1,"front":"From the chosen angle, what is the non-hypotenuse side next to it called?","back":"The adjacent side.","mcqOptions":[{"text":"The adjacent side.","correct":true,"explanation":"The adjacent side touches the chosen acute angle and is not the hypotenuse. Its label can change when a different focus angle is selected."},{"text":"The opposite side.","correct":false,"explanation":"The opposite side lies directly across from the chosen angle rather than next to it. The non-hypotenuse side touching the angle is adjacent."},{"text":"The hypotenuse side.","correct":false,"explanation":"The hypotenuse touches each acute angle, but it is excluded by the question and is always opposite $90^\\circ$. The other neighbouring side is adjacent."},{"text":"The base side.","correct":false,"explanation":"“Base” depends on the triangle’s orientation and is not a SOHCAHTOA side label. The non-hypotenuse side next to the chosen angle is adjacent."}]},{"id":"f0693322-ab2e-4dea-8ef0-431cc60645ef","cardType":"cloze","points":null,"front":"Changing the focus angle can swap [ ], but the [ ] stays the same.","back":"Changing the focus angle can swap opposite and adjacent, but the hypotenuse stays the same.","mcqOptions":[{"text":"Changing the focus angle can swap opposite and adjacent, but the hypotenuse stays the same.","correct":true,"explanation":"Opposite and adjacent are defined relative to the selected acute angle, so they can exchange labels. The hypotenuse remains opposite the fixed $90^\\circ$ angle."},{"text":"Changing the focus angle can swap hypotenuse and adjacent, but the hypotenuse stays the same.","correct":false,"explanation":"The hypotenuse is fixed as the side opposite $90^\\circ$, so it cannot swap with the adjacent side. Only opposite and adjacent depend on the focus angle."},{"text":"Changing the focus angle can swap opposite and adjacent, but the opposite stays the same.","correct":false,"explanation":"Although opposite and adjacent can swap when the focus angle changes, the opposite side does not remain fixed. The hypotenuse always stays the same."},{"text":"Changing the focus angle can swap opposite and hypotenuse, but the adjacent stays the same.","correct":false,"explanation":"The hypotenuse cannot become an angle-dependent side, and the adjacent side does not remain fixed. Opposite and adjacent swap, while the hypotenuse stays unchanged."}]},{"id":"214ba1ef-4c14-4c4a-b5ee-ead44e9a0795","cardType":"cloze","points":null,"front":"$$\\sin\\theta$ uses [ ] over [ ].","back":"$$\\sin\\theta$ uses opposite over hypotenuse.","mcqOptions":[{"text":"$$\\sin\\theta$ uses opposite over hypotenuse.","correct":true,"explanation":"The mnemonic SOH means sine equals opposite divided by hypotenuse, so $\\sin\\theta=\\frac{\\text{opposite}}{\\text{hypotenuse}}$."},{"text":"$$\\sin\\theta$ uses adjacent over hypotenuse.","correct":false,"explanation":"Adjacent over hypotenuse is the cosine ratio, represented by CAH. Sine follows SOH, so it uses opposite over hypotenuse."},{"text":"$$\\sin\\theta$ uses opposite over adjacent.","correct":false,"explanation":"Opposite over adjacent is the tangent ratio, represented by TOA. Sine follows SOH, so its denominator is the hypotenuse."},{"text":"$$\\sin\\theta$ uses hypotenuse over opposite.","correct":false,"explanation":"This reverses the sine ratio, producing the reciprocal of sine rather than sine itself. SOH gives opposite over hypotenuse."}]},{"id":"cff95125-07d9-4953-976e-86630719698c","cardType":"cloze","points":null,"front":"$$\\cos\\theta$ uses [ ] over [ ].","back":"$$\\cos\\theta$ uses adjacent over hypotenuse.","mcqOptions":[{"text":"$$\\cos\\theta$ uses adjacent over hypotenuse.","correct":true,"explanation":"The mnemonic CAH means cosine equals adjacent divided by hypotenuse, so $\\cos\\theta=\\frac{\\text{adjacent}}{\\text{hypotenuse}}$."},{"text":"$$\\cos\\theta$ uses opposite over hypotenuse.","correct":false,"explanation":"Opposite over hypotenuse is the sine ratio, represented by SOH. Cosine follows CAH, so it uses adjacent over hypotenuse."},{"text":"$$\\cos\\theta$ uses adjacent over opposite.","correct":false,"explanation":"Adjacent over opposite is the reciprocal of tangent, not cosine. CAH states that cosine uses adjacent over hypotenuse."},{"text":"$$\\cos\\theta$ uses hypotenuse over adjacent.","correct":false,"explanation":"This reverses the cosine ratio, giving the reciprocal of cosine rather than cosine itself. CAH gives adjacent over hypotenuse."}]},{"id":"816145f2-dd14-40cc-a012-140074aa71c5","cardType":"cloze","points":null,"front":"$$\\tan\\theta$ uses [ ] over [ ].","back":"$$\\tan\\theta$ uses opposite over adjacent.","mcqOptions":[{"text":"$$\\tan\\theta$ uses opposite over adjacent.","correct":true,"explanation":"The mnemonic TOA means tangent equals opposite divided by adjacent, so $\\tan\\theta=\\frac{\\text{opposite}}{\\text{adjacent}}$."},{"text":"$$\\tan\\theta$ uses opposite over hypotenuse.","correct":false,"explanation":"Opposite over hypotenuse is the sine ratio, not tangent. TOA shows that tangent uses opposite over adjacent."},{"text":"$$\\tan\\theta$ uses adjacent over hypotenuse.","correct":false,"explanation":"Adjacent over hypotenuse is the cosine ratio, represented by CAH. Tangent follows TOA, so it uses opposite over adjacent."},{"text":"$$\\tan\\theta$ uses adjacent over opposite.","correct":false,"explanation":"This reverses the tangent ratio and gives the reciprocal of tangent. TOA places opposite above adjacent, not adjacent above opposite."}]},{"id":"62fcff57-f1c5-40a3-a65e-3d58c4a08134","cardType":"basic","points":1,"front":"What does $\\theta$ usually mean in SOHCAHTOA?","back":"The angle.","mcqOptions":[{"text":"The angle.","correct":true,"explanation":"The symbol $\\theta$ conventionally represents the angle being considered. Identifying this angle allows the opposite, adjacent and hypotenuse sides to be labelled correctly."},{"text":"The hypotenuse.","correct":false,"explanation":"The hypotenuse is a side of the right-angled triangle, not the quantity represented by $\\theta$. In SOHCAHTOA, $\\theta$ normally denotes the angle being used."},{"text":"The opposite side.","correct":false,"explanation":"The opposite side is identified relative to $\\theta$, but it is not represented by that symbol. The symbol $\\theta$ normally means the angle."},{"text":"The right angle.","correct":false,"explanation":"The right angle is fixed at $90^\\circ$ and is usually marked with a square. The symbol $\\theta$ normally denotes the other angle being considered."}]},{"id":"d35d00f4-66da-4629-90a8-965b5832b198","cardType":"basic","points":2,"front":"Angle $35^\\circ$, opposite $20\\text{ cm}$, hypotenuse $x$: what expression gives $x$?","back":"$x=\\frac{20}{\\sin 35^\\circ}$","mcqOptions":[{"text":"$x=\\frac{20}{\\sin 35^\\circ}$","correct":true,"explanation":"Using $\\sin\\theta=\\frac{\\text{opposite}}{\\text{hypotenuse}}$ gives $\\sin35^\\circ=\\frac{20}{x}$. Rearranging by multiplying by $x$ and dividing by $\\sin35^\\circ$ gives this expression."},{"text":"$x=20\\sin 35^\\circ$","correct":false,"explanation":"This multiplies by the sine value instead of dividing by it. From $\\sin35^\\circ=\\frac{20}{x}$, rearrangement gives $x=\\frac{20}{\\sin35^\\circ}$."},{"text":"$x=\\frac{20}{\\cos 35^\\circ}$","correct":false,"explanation":"Cosine relates the adjacent side to the hypotenuse, but the given side is opposite the angle. Sine is required, giving $x=\\frac{20}{\\sin35^\\circ}$."},{"text":"$x=\\frac{\\sin 35^\\circ}{20}$","correct":false,"explanation":"This reverses the quantities when rearranging and would not produce a length of the correct size. The hypotenuse is $x=\\frac{20}{\\sin35^\\circ}$."}]},{"id":"ddfc18e8-041e-4527-95eb-dbceb9c214e5","cardType":"basic","points":2,"front":"Angle $42^\\circ$, opposite $11\\text{ cm}$, adjacent $x$: what expression gives $x$?","back":"$x=\\frac{11}{\\tan 42^\\circ}$","mcqOptions":[{"text":"$x=\\frac{11}{\\tan 42^\\circ}$","correct":true,"explanation":"Using $\\tan\\theta=\\frac{\\text{opposite}}{\\text{adjacent}}$ gives $\\tan42^\\circ=\\frac{11}{x}$. Rearranging by multiplying by $x$ and dividing by $\\tan42^\\circ$ produces this expression."},{"text":"$x=11\\tan 42^\\circ$","correct":false,"explanation":"This multiplies by the tangent value rather than dividing by it. Rearranging $\\tan42^\\circ=\\frac{11}{x}$ gives $x=\\frac{11}{\\tan42^\\circ}$."},{"text":"$x=\\frac{11}{\\sin 42^\\circ}$","correct":false,"explanation":"Sine requires the opposite side and hypotenuse, but the known sides here are opposite and adjacent. Tangent must be used, giving $x=\\frac{11}{\\tan42^\\circ}$."},{"text":"$x=\\frac{\\tan 42^\\circ}{11}$","correct":false,"explanation":"This incorrectly reverses the numerator and denominator during rearrangement. Starting from $\\tan42^\\circ=\\frac{11}{x}$ leads to $x=\\frac{11}{\\tan42^\\circ}$."}]},{"id":"ab2fd155-1f01-423b-9251-6dfad34a5b4e","cardType":"cloze","points":null,"front":"For IGCSE trigonometry, the calculator should normally be in [ ] mode, not [ ].","back":"For IGCSE trigonometry, the calculator should normally be in degrees mode, not radians.","mcqOptions":[{"text":"For IGCSE trigonometry, the calculator should normally be in degrees mode, not radians.","correct":true,"explanation":"IGCSE triangle angles are normally stated in degrees, as shown by the $^\\circ$ symbol. Radian mode would therefore produce incorrect trigonometric values."},{"text":"For IGCSE trigonometry, the calculator should normally be in radians mode, not degrees.","correct":false,"explanation":"This reverses the required calculator settings. IGCSE triangle questions normally measure angles in degrees, so the calculator should use degrees rather than radians."},{"text":"For IGCSE trigonometry, the calculator should normally be in gradians mode, not radians.","correct":false,"explanation":"Gradians divide a full turn into 400 units and are not normally used in IGCSE triangle questions. The appropriate setting is degrees, not radians."},{"text":"For IGCSE trigonometry, the calculator should normally be in radians mode, not gradians.","correct":false,"explanation":"Radian mode is common in advanced mathematics but not for ordinary IGCSE triangle angles marked with $^\\circ$. The calculator should normally use degrees, not gradians."}]},{"id":"19f631ff-4012-4375-a91a-8efc944001ea","cardType":"basic","points":1,"front":"If the angle is unknown, what type of trig button is usually needed?","back":"An inverse trig button.","mcqOptions":[{"text":"An inverse trig button.","correct":true,"explanation":"When a side ratio is known and the angle is required, an inverse sine, cosine or tangent function reverses the relevant trigonometric relationship."},{"text":"An ordinary trig button.","correct":false,"explanation":"An ordinary trig button converts a known angle into a side ratio rather than recovering an angle. An inverse trig button is needed when the angle is unknown."},{"text":"A logarithm button.","correct":false,"explanation":"A logarithm button reverses exponentiation, not a trigonometric ratio. To recover an angle from a side ratio, the corresponding inverse trig button is required."},{"text":"A square root button.","correct":false,"explanation":"A square root button reverses squaring and cannot recover an angle from a trigonometric ratio. The required operation is an inverse trig function."}]},{"id":"fb9f6c52-9b89-4505-b5db-3cec9dd07c3d","cardType":"basic","points":2,"front":"Adjacent $16\\text{ cm}$, hypotenuse $24\\text{ cm}$, angle $x$: what inverse expression finds $x$?","back":"$x=\\cos^{-1}\\left(\\frac{16}{24}\\right)$","mcqOptions":[{"text":"$x=\\cos^{-1}\\left(\\frac{16}{24}\\right)$","correct":true,"explanation":"Cosine uses adjacent over hypotenuse, so $\\cos x=\\frac{16}{24}$. Applying inverse cosine to both sides gives the required expression for $x$."},{"text":"$x=\\sin^{-1}\\left(\\frac{16}{24}\\right)$","correct":false,"explanation":"Sine uses opposite over hypotenuse, but $16$ is the adjacent side. Cosine is therefore required: $x=\\cos^{-1}\\left(\\frac{16}{24}\\right)$."},{"text":"$x=\\cos^{-1}\\left(\\frac{24}{16}\\right)$","correct":false,"explanation":"This reverses adjacent over hypotenuse, producing a ratio greater than $1$, for which inverse cosine has no real angle. The ratio must be $\\frac{16}{24}$."},{"text":"$x=\\cos\\left(\\frac{16}{24}\\right)$","correct":false,"explanation":"Ordinary cosine converts an angle into a ratio; it does not convert a ratio back into an angle. The inverse expression is $x=\\cos^{-1}\\left(\\frac{16}{24}\\right)$."}]},{"id":"12dcea2a-9075-4ea5-953f-8f59132a54a7","cardType":"basic","points":2,"front":"Opposite $11\\text{ cm}$, adjacent $15\\text{ cm}$, angle $x$: what inverse expression finds $x$?","back":"$x=\\tan^{-1}\\left(\\frac{11}{15}\\right)$","mcqOptions":[{"text":"$x=\\tan^{-1}\\left(\\frac{11}{15}\\right)$","correct":true,"explanation":"Tangent uses opposite over adjacent, so $\\tan x=\\frac{11}{15}$. Applying inverse tangent gives the angle expression shown."},{"text":"$x=\\tan^{-1}\\left(\\frac{15}{11}\\right)$","correct":false,"explanation":"This reverses the tangent ratio by placing adjacent over opposite. Tangent requires opposite over adjacent, so the correct expression uses $\\frac{11}{15}$."},{"text":"$x=\\sin^{-1}\\left(\\frac{11}{15}\\right)$","correct":false,"explanation":"Inverse sine requires an opposite-to-hypotenuse ratio, but $15$ is the adjacent side. With opposite and adjacent known, use $x=\\tan^{-1}\\left(\\frac{11}{15}\\right)$."},{"text":"$x=\\cos^{-1}\\left(\\frac{11}{15}\\right)$","correct":false,"explanation":"Inverse cosine requires an adjacent-to-hypotenuse ratio, but $11$ and $15$ are opposite and adjacent. Their correct relationship is tangent, using opposite over adjacent."}]},{"id":"14914b35-9ec9-4bca-99c4-0dae3643569e","cardType":"cloze","points":null,"front":"Inverse trig works backwards from a side ratio to find an [ ]; $\\tan^{-1}$ does not mean [ ].","back":"Inverse trig works backwards from a side ratio to find an angle; $\\tan^{-1}$ does not mean one divided by tangent.","mcqOptions":[{"text":"Inverse trig works backwards from a side ratio to find an angle; $\\tan^{-1}$ does not mean one divided by tangent.","correct":true,"explanation":"An inverse trigonometric function converts a known side ratio back into its corresponding angle. The superscript $-1$ denotes an inverse function, not a reciprocal."},{"text":"Inverse trig works backwards from a side ratio to find a side length; $\\tan^{-1}$ does not mean one divided by tangent.","correct":false,"explanation":"A side ratio and inverse trig function determine an angle, not a side length. The notation $\\tan^{-1}$ means inverse tangent rather than one divided by tangent."},{"text":"Inverse trig works backwards from a side ratio to find an angle; $\\tan^{-1}$ does not mean inverse tangent.","correct":false,"explanation":"Inverse trig does recover an angle, but the second statement wrongly denies the meaning of the notation. Here, $\\tan^{-1}$ means inverse tangent, not a reciprocal."},{"text":"Inverse trig works backwards from a side ratio to find a side length; $\\tan^{-1}$ does not mean inverse tangent.","correct":false,"explanation":"Both completions confuse inverse functions with finding sides. Inverse trig finds an angle from a ratio, and $\\tan^{-1}$ means inverse tangent rather than one divided by tangent."}]},{"id":"c145d710-f2b6-4af1-984e-c1953e6d613b","cardType":"basic","points":1,"front":"For angle $ABC$, which point is the angle at?","back":"Point $B$.","mcqOptions":[{"text":"Point $B$.","correct":true,"explanation":"In angle $ABC$, the middle letter identifies the vertex where the angle is formed, so the angle is at point $B$."},{"text":"Point $A$.","correct":false,"explanation":"The first letter names one arm of the angle, not its vertex. In angle $ABC$, the middle letter is the vertex, so the angle is at point $B$."},{"text":"Point $C$.","correct":false,"explanation":"The final letter names the other arm of the angle, not its vertex. In angle $ABC$, the middle letter identifies the vertex, so the angle is at point $B$."},{"text":"Point $AC$.","correct":false,"explanation":"An angle is located at a single vertex, not along a side such as $AC$. In angle $ABC$, the middle letter shows that the vertex is point $B$."}]},{"id":"f8aa3863-4e0e-455b-88f7-2fcc9b7ef976","cardType":"basic","points":2,"front":"Triangle $ABC$ is right-angled at $B$, $BC=20\\text{ cm}$ and angle $C=35^\\circ$. What equation finds $AB$?","back":"$\\tan 35^\\circ=\\frac{AB}{20}$","mcqOptions":[{"text":"$\\tan 35^\\circ=\\frac{AB}{20}$","correct":true,"explanation":"Relative to angle $C$, $AB$ is the opposite side and $BC=20$ is the adjacent side. Therefore, tangent gives opposite over adjacent: $\\tan 35^\\circ=\\frac{AB}{20}$."},{"text":"$\\sin 35^\\circ=\\frac{AB}{20}$","correct":false,"explanation":"Sine compares opposite with the hypotenuse, but $20$ is the adjacent side here. The correct ratio uses tangent: $\\tan 35^\\circ=\\frac{AB}{20}$."},{"text":"$\\tan 35^\\circ=\\frac{20}{AB}$","correct":false,"explanation":"This reverses the tangent ratio, using adjacent over opposite instead of opposite over adjacent. The correct equation is $\\tan 35^\\circ=\\frac{AB}{20}$."},{"text":"$\\cos 35^\\circ=\\frac{AB}{20}$","correct":false,"explanation":"Cosine compares adjacent with the hypotenuse, whereas $AB$ is opposite angle $C$ and $20$ is adjacent. The correct equation is $\\tan 35^\\circ=\\frac{AB}{20}$."}]},{"id":"8d95174c-cb5a-4b86-87d4-57dd85c4303f","cardType":"basic","points":1,"front":"A trapezium has vertical sides $4\\text{ m}$ and $6\\text{ m}$. What is the small triangle’s vertical height?","back":"$2\\text{ m}$","mcqOptions":[{"text":"$2\\text{ m}$","correct":true,"explanation":"The small triangle’s vertical height is the difference between the two vertical sides: $6-4=2\\text{ m}$."},{"text":"$10\\text{ m}$","correct":false,"explanation":"Adding the two vertical sides gives the total of both lengths, not the height difference forming the small triangle. The required height is $6-4=2\\text{ m}$."},{"text":"$5\\text{ m}$","correct":false,"explanation":"Averaging the two vertical sides does not find the extra height of the small triangle. Subtract the shorter side from the longer side to get $6-4=2\\text{ m}$."},{"text":"$4\\text{ m}$","correct":false,"explanation":"Using the shorter vertical side ignores the additional height represented by the difference between the sides. The small triangle’s vertical height is $6-4=2\\text{ m}$."}]},{"id":"a7ae28da-041d-4777-b756-fc7e9ea12276","cardType":"basic","points":2,"front":"Small right triangle: opposite $2\\text{ m}$, adjacent $15\\text{ m}$. What equation finds the angle $\\theta$ above the horizontal?","back":"$\\tan\\theta=\\frac{2}{15}$","mcqOptions":[{"text":"$\\tan\\theta=\\frac{2}{15}$","correct":true,"explanation":"For the angle above the horizontal, the vertical side of $2\\text{ m}$ is opposite and the horizontal side of $15\\text{ m}$ is adjacent. Tangent is opposite over adjacent."},{"text":"$\\sin\\theta=\\frac{2}{15}$","correct":false,"explanation":"Sine requires the hypotenuse, but $15\\text{ m}$ is the adjacent horizontal side. Since the given sides are opposite and adjacent, the correct equation is $\\tan\\theta=\\frac{2}{15}$."},{"text":"$\\tan\\theta=\\frac{15}{2}$","correct":false,"explanation":"The sides have been placed in the reverse order, giving adjacent over opposite. Tangent uses opposite over adjacent, so the correct equation is $\\tan\\theta=\\frac{2}{15}$."},{"text":"$\\cos\\theta=\\frac{2}{15}$","correct":false,"explanation":"Cosine compares adjacent with hypotenuse, not opposite with adjacent. Here the relevant ratio is tangent, giving $\\tan\\theta=\\frac{2}{15}$."}]},{"id":"b541a8ec-c11b-4239-bc73-10d82b7c458d","cardType":"basic","points":2,"front":"If the angle to the horizontal is $7.6^\\circ$, what is the angle to the vertical?","back":"$82.4^\\circ$","mcqOptions":[{"text":"$82.4^\\circ$","correct":true,"explanation":"The horizontal and vertical directions are perpendicular, so their angles add to $90^\\circ$. Thus the angle to the vertical is $90-7.6=82.4^\\circ$."},{"text":"$97.6^\\circ$","correct":false,"explanation":"Adding $7.6^\\circ$ to $90^\\circ$ gives the reflex-style value $97.6^\\circ$, but the acute complementary angle is required. It is $90-7.6=82.4^\\circ$."},{"text":"$7.6^\\circ$","correct":false,"explanation":"The angle to the vertical is not equal to the angle to the horizontal because the reference directions are perpendicular. The two angles are complementary, giving $90-7.6=82.4^\\circ$."},{"text":"$172.4^\\circ$","correct":false,"explanation":"Subtracting $7.6^\\circ$ from $180^\\circ$ finds a supplementary angle, not the angle between the line and the vertical. The required complementary angle is $82.4^\\circ$."}]},{"id":"5b27e82f-cd0d-4f3f-88f7-a4bdb752caef","cardType":"cloze","points":null,"front":"When asked for 1 decimal place, keep the [ ] and round only at the [ ].","back":"When asked for 1 decimal place, keep the full calculator value and round only at the final line.","mcqOptions":[{"text":"When asked for 1 decimal place, keep the full calculator value and round only at the final line.","correct":true,"explanation":"Keeping the full calculator value avoids cumulative rounding errors. Round only the final result to 1 decimal place, after all calculations have been completed."},{"text":"When asked for 1 decimal place, keep the first decimal place and round only at the first step.","correct":false,"explanation":"Rounding at the first step can change later calculations and produce an inaccurate final answer. Keep the full calculator value and round only at the final line."},{"text":"When asked for 1 decimal place, keep the full calculator value and round only at the first step.","correct":false,"explanation":"Although retaining the full value initially is correct, rounding at the first step introduces avoidable error into subsequent work. Round only at the final line."},{"text":"When asked for 1 decimal place, keep the first decimal place and round only at the final line.","correct":false,"explanation":"Keeping only one decimal place discards useful calculator accuracy before the calculation is finished. Keep the full calculator value, then round only at the final line."}]},{"id":"b7063766-8f79-4c51-b825-d5460530fd4e","cardType":"basic","points":1,"front":"A right triangle gives both shorter sides and asks for the hypotenuse. Which method is quickest?","back":"Pythagoras.","mcqOptions":[{"text":"Pythagoras.","correct":true,"explanation":"When both shorter sides of a right-angled triangle are known, Pythagoras’ theorem finds the hypotenuse directly using $a^2+b^2=c^2$."},{"text":"Sine rule.","correct":false,"explanation":"The sine rule is mainly used when the triangle is not necessarily right-angled and includes known opposite side-angle pairs. For two shorter sides of a right triangle, use Pythagoras."},{"text":"Cosine rule.","correct":false,"explanation":"The cosine rule can find a missing side but is unnecessary here and is usually used for non-right-angled triangles. With both shorter sides known in a right triangle, use Pythagoras."},{"text":"SOHCAHTOA.","correct":false,"explanation":"SOHCAHTOA relates a side to a known acute angle, but no angle is needed when both shorter sides are given. Pythagoras is the quickest method for finding the hypotenuse."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"SOHCAHTOA (Trigonometry)","title":"SOHCAHTOA (Trigonometry) Flashcards","topbar":{"backHref":"/igcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"c3a73f54-72a9-475c-a240-7b9435772505","walled":"$L39"}],"$L3a","$L3b"]