Flashcards","topicId":"a76e1bdf-e924-4e5a-94a5-65d90124696a","topicSlug":"trigonometry-9","cards":[{"id":"5546ac61-52bd-4a4f-bc65-697f1a845fab","cardType":"cloze","front":"A complete turn is [ ], so a half-turn is $\\pi$ radians.","back":"A complete turn is $2\\pi$ radians, so a half-turn is $\\pi$ radians.","points":null,"mcqOptions":null},{"id":"3b04daea-c068-46a0-9f35-a97a8365f6db","cardType":"cloze","front":"A complete turn is $2\\pi$ radians, so a half-turn is [ ].","back":"A complete turn is $2\\pi$ radians, so a half-turn is $\\pi$ radians.","points":null,"mcqOptions":null},{"id":"fd51f064-ad50-441f-adcc-aaa3d9da5aaf","cardType":"basic","front":"An arc has the same length as its circle's radius. What angle does it subtend at the centre?","back":"1 radian.","points":1,"mcqOptions":null},{"id":"a037a91f-a02a-4145-8356-726d1abdb058","cardType":"cloze","front":"To convert degrees to radians, multiply by $\\text{[...]}$. To convert radians to degrees, multiply by $\\frac{180}{\\pi}$.","back":"To convert degrees to radians, multiply by $\\boxed{\\frac{\\pi}{180}}$. To convert radians to degrees, multiply by $\\frac{180}{\\pi}$.","points":null,"mcqOptions":null},{"id":"97232fcb-231d-48b6-ba81-99bfd4cd31bb","cardType":"cloze","front":"To convert degrees to radians, multiply by $\\frac{\\pi}{180}$. To convert radians to degrees, multiply by $\\text{[...]}$.","back":"To convert degrees to radians, multiply by $\\frac{\\pi}{180}$. To convert radians to degrees, multiply by $\\boxed{\\frac{180}{\\pi}}$.","points":null,"mcqOptions":null},{"id":"a2acd806-e9e7-4ffd-bb69-53f394cc12b6","cardType":"cloze","front":"For $\\theta$ in radians, the arc length is $\\text{[...]}$ and the sector area is $A=\\frac12r^2\\theta$.","back":"For $\\theta$ in radians, the arc length is $\\boxed{s=r\\theta}$ and the sector area is $A=\\frac12r^2\\theta$.","points":null,"mcqOptions":null},{"id":"914da347-e22e-4eee-970f-9a957894e818","cardType":"cloze","front":"For $\\theta$ in radians, the arc length is $s=r\\theta$ and the sector area is $\\text{[...]}$.","back":"For $\\theta$ in radians, the arc length is $s=r\\theta$ and the sector area is $\\boxed{A=\\frac12r^2\\theta}$.","points":null,"mcqOptions":null},{"id":"9ce83c64-3279-4ca7-ae9c-5a3f9c9160b4","cardType":"basic","front":"Why is a complete turn equal to $2\\pi$ radians?","back":"$$\\theta=\\frac{s}{r}=\\frac{2\\pi r}{r}=\\boldsymbol{2\\pi}$.","points":2,"mcqOptions":null},{"id":"4d8fff27-e7e0-41d6-a68a-9cc34ec023f2","cardType":"basic","front":"Convert $135^\\circ$ to radians.","back":"$\\frac{3\\pi}{4}$ radians.","points":2,"mcqOptions":null},{"id":"d66c9d4e-f43b-4986-8751-b717057cb116","cardType":"basic","front":"Convert $\\frac{7\\pi}{12}$ radians to degrees.","back":"$105^\\circ$.","points":2,"mcqOptions":null},{"id":"e7e255e6-db6e-45e0-8993-706f9d7393f5","cardType":"basic","front":"If $\\theta=\\frac{\\pi}{3}$ is written without a degree symbol, which angle unit is implied?","back":"Radians.","points":1,"mcqOptions":null},{"id":"7243e5a7-dabf-486c-822a-f0a9cef04e8b","cardType":"basic","front":"Which calculator mode should be used when an angle is an exact multiple of $\\pi$?","back":"Radian mode.","points":1,"mcqOptions":null},{"id":"e9228e3d-ab59-479b-9a8b-03875e6b6bc7","cardType":"basic","front":"A sector has radius $8$ cm and angle $\\frac{5\\pi}{12}$. Find its arc length.","back":"$\\frac{10\\pi}{3}$ cm.","points":2,"mcqOptions":null},{"id":"b1ab6757-f19f-4a34-ab74-545ba36949e8","cardType":"basic","f

3.4.1 Trigonometry (A-level only) Flashcards

3.4.1 Trigonometry (A-level only) Flashcards