Flashcards","topicId":"cbc5211d-47b5-4b58-b978-00f0a36a6d24","topicSlug":"trigonometry-15","cards":[{"id":"b5512957-4099-4ecd-a84d-4add2d6658cf","cardType":"cloze","front":"A trigonometric identity is true for [ ] of the variable.","back":"A trigonometric identity is true for all permissible values of the variable.","points":null,"mcqOptions":null},{"id":"8e13c3a4-9d29-411b-af96-1666ec00ff2e","cardType":"basic","front":"Why do checks at several values of $x$ not prove an identity?","back":"They do not establish the result for every permissible value.","points":2,"mcqOptions":null},{"id":"5d622424-1736-4d12-afda-eaccb285302d","cardType":"cloze","front":"The Pythagorean identity is $\\text{[...]}$.","back":"The Pythagorean identity is $\\boxed{\\sin^2x+\\cos^2x\\equiv1}$.","points":null,"mcqOptions":null},{"id":"15e80c8b-cc83-4abd-b007-062c2fa3afb9","cardType":"cloze","front":"The quotient identity is $\\tan x\\equiv$ $\\text{[...]}$.","back":"The quotient identity is $\\tan x\\equiv$ $\\boxed{\\frac{\\sin x}{\\cos x}}$.","points":null,"mcqOptions":null},{"id":"a624d437-f0e9-4026-ae38-324127133d4a","cardType":"cloze","front":"The reciprocal identity for secant is $\\sec x\\equiv$ $\\text{[...]}$.","back":"The reciprocal identity for secant is $\\sec x\\equiv$ $\\boxed{\\frac{1}{\\cos x}}$.","points":null,"mcqOptions":null},{"id":"84794344-8866-4c72-850a-c334b6249691","cardType":"cloze","front":"The reciprocal identity for cosecant is $\\cosec x\\equiv$ $\\text{[...]}$.","back":"The reciprocal identity for cosecant is $\\cosec x\\equiv$ $\\boxed{\\frac{1}{\\sin x}}$.","points":null,"mcqOptions":null},{"id":"11ba9fea-48e8-4046-a504-ac899536c6bb","cardType":"basic","front":"How is $1+\\tan^2x\\equiv\\sec^2x$ derived from the Pythagorean identity?","back":"Divide every term by $\\cos^2x$.","points":2,"mcqOptions":null},{"id":"9fa3123f-e891-4301-a4db-b9a153059a7f","cardType":"basic","front":"What identity links $\\tan^2x$ and $\\sec^2x$?","back":"$1+\\tan^2x\\equiv\\sec^2x$","points":1,"mcqOptions":null},{"id":"3cda71d6-7f1c-4c25-a395-76f95ae86acf","cardType":"basic","front":"What identity links $\\cot^2x$ and $\\cosec^2x$?","back":"$1+\\cot^2x\\equiv\\cosec^2x$","points":1,"mcqOptions":null},{"id":"26a2aeff-c7d0-4427-ab2e-f1f2f268835d","cardType":"basic","front":"Which side should usually begin an identity proof?","back":"The more complicated side.","points":1,"mcqOptions":null},{"id":"fb037be9-d37e-4f3c-8bd4-fe500b8d6dd0","cardType":"basic","front":"Why should an identity proof not manipulate both sides simultaneously?","back":"It assumes the identity before proving it.","points":2,"mcqOptions":null},{"id":"8d5c43ad-371c-4648-9769-8e17cbead87d","cardType":"basic","front":"What common denominator combines $\\frac1{1-\\sin x}+\\frac1{1+\\sin x}$?","back":"$(1-\\sin x)(1+\\sin x)$","points":1,"mcqOptions":null},{"id":"2403be19-17b2-4285-98a0-afb0d0a4e7f8","cardType":"basic","front":"Why can $\\sin x$ not be cancelled from $\\frac{1+\\sin x}{\\sin x}$?","back":"Cancellation applies to common factors, not terms across addition.","points":2,"mcqOptions":null},{"id":"dcb434d4-dc8c-4f8e-a84c-65324924149e","cardType":"cloze","front":"The sine compound-angle identity is $\\text{[...]}$.","back":"The sine compound-angle identity is $\\boxed{\\sin(A\\pm B)\\equiv\\sin A\\cos B\\pm\\cos A\\sin B}$.","points":null,"mcqOptions":null},{"id":"1c3fa01a-40c3-4db7-a47c-1edc815d633e","cardType":"cloze","front":"The cosine compound-angle identity is $\\text{[...]}$.","back":"The cosine compound-angle identity is $\\boxed{\\cos(A\\pm B)\\equiv\\cos A\\cos B\\mp\\sin A\\sin B}$.","points":null,"mcqOptions":null},{"id":"07ef32b9-f176-4872-b4e2-3afa257633bd","cardType":"basic","front":"State the tangent addition identity.","back":"$\\tan(A+B)\\equiv\\frac{\\tan A+\\tan B}{1-\\tan A\\tan B}$",

3.4.7 Trigonometry (A-level only) Flashcards

3.4.7 Trigonometry (A-level only) Flashcards