6-f602-4e7c-b02a-e48c7f473dd0","topicSlug":"trigonometry-3","cards":[{"id":"9c151b53-19be-456c-8c6c-f376b9dbece7","cardType":"basic","front":"Which side is paired with angle $A$?","back":"Side $a$, directly opposite $A$.","points":1,"mcqOptions":null},{"id":"2c7ca170-421a-4671-830c-d067802a940f","cardType":"basic","front":"Which angle is included between sides $b$ and $c$?","back":"Angle $A$.","points":1,"mcqOptions":null},{"id":"ca572a51-a592-49f7-b0ce-e7154272b2e9","cardType":"cloze","front":"The interior angles of a triangle satisfy $\\text{[...]}$.","back":"The interior angles of a triangle satisfy $\\boxed{A+B+C=180^\\circ}$.","points":null,"mcqOptions":null},{"id":"dfb34735-bb93-4f8a-b541-b89c8c68669c","cardType":"basic","front":"What calculator mode is required when angles are given in degrees?","back":"Degree mode.","points":1,"mcqOptions":null},{"id":"2378b6c2-7c20-4864-9ad3-f14f9c8f26ea","cardType":"cloze","front":"The side-first sine rule is $\\text{[...]}$.","back":"The side-first sine rule is $\\boxed{\\frac{a}{\\sin A}=\\frac{b}{\\sin B}=\\frac{c}{\\sin C}}$.","points":null,"mcqOptions":null},{"id":"022ddf4b-d1ea-4500-9502-0aa65a49da09","cardType":"basic","front":"What known pairing is needed to use the sine rule?","back":"A complete opposite side-angle pair.","points":1,"mcqOptions":null},{"id":"a04e13f0-0e67-4a82-9c29-fdd90edbd3dd","cardType":"basic","front":"Which rule is usually appropriate for AAS or ASA information?","back":"The sine rule.","points":1,"mcqOptions":null},{"id":"e5542591-77b8-4b86-9169-7c2147cfe642","cardType":"basic","front":"Which sine-rule arrangement is easiest when finding a side?","back":"Put the sides on top: $\\frac{a}{\\sin A}=\\frac{b}{\\sin B}$.","points":1,"mcqOptions":null},{"id":"dfdf57f9-8813-47aa-acf7-54bb7a79cf17","cardType":"basic","front":"Which sine-rule arrangement is easiest when finding an angle?","back":"Put the sines on top: $\\frac{\\sin A}{a}=\\frac{\\sin B}{b}$.","points":1,"mcqOptions":null},{"id":"5252009b-5b3b-4635-8436-8ef6d54e1847","cardType":"basic","front":"Angle $B$ is larger than angle $A$. Predict the relationship between $b$ and $a$.","back":"$b>a$, because the larger angle has the longer opposite side.","points":2,"mcqOptions":null},{"id":"c7596891-d63a-4ac1-b886-f601c01033be","cardType":"cloze","front":"Supplementary angles have the same sine: $\\text{[...]}$.","back":"Supplementary angles have the same sine: $\\boxed{\\sin\\theta=\\sin(180^\\circ-\\theta)}$.","points":null,"mcqOptions":null},{"id":"4824d383-635e-48a9-b8de-d23964fd60df","cardType":"basic","front":"Why can SSA information produce two possible triangles?","back":"The acute angle and its supplementary angle have equal sines.","points":2,"mcqOptions":null},{"id":"aff23e48-7d00-4e7b-a985-3a8bd7aec188","cardType":"basic","front":"After inverse sine gives $\\theta$, which second angle must be tested?","back":"$180^\\circ-\\theta$.","points":1,"mcqOptions":null},{"id":"df765455-c6ca-49bb-ab6a-fa681b637f4a","cardType":"basic","front":"How is a supplementary sine-rule solution tested for validity?","back":"Check that the triangle's angles still total $180^\\circ$.","points":2,"mcqOptions":null},{"id":"75d566a6-1023-4374-b303-ee40a7abb5ed","cardType":"basic","front":"What does a result such as $\\sin B>1$ imply?","back":"No triangle is possible.","points":1,"mcqOptions":null},{"id":"ec2acd9c-4866-466c-b9de-c6e93f183df0","cardType":"cloze","front":"For side $a$ opposite included angle $A$, the cosine rule is $\\text{[...]}$.","back":"For side $a$ opposite included angle $A$, the cosine rule is $\\boxed{a^2=b^2+c^2-2bc\\cos A}$.","points":null,"mcqOptions":null},{"id":"fad3bc12-871a-4b48-8635-0ca6d81a49f1","cardType":"basic","front":"Which rule should be used to find a third side from SAS information?","back":"The cosine rule.","points":1,"mcqOptions":null},{"id":"b0f3a

1.4.2 Trigonometry Flashcards

1.4.2 Trigonometry Flashcards