s Flashcards","topicId":"c081b43c-6d21-4856-83de-300c34e7ef01","topicSlug":"trigonometric-identities","cards":[{"id":"5128219f-dfc4-43c2-9ab9-c9d9767c1687","cardType":"cloze","front":"The reciprocal function of cosine is $\\text{[...]}$.","back":"The reciprocal function of cosine is $\\boxed{\\sec\\theta=\\frac{1}{\\cos\\theta}}$.","points":null,"mcqOptions":null},{"id":"60d91b23-901d-402e-9a81-52a919810670","cardType":"cloze","front":"The reciprocal function of sine is $\\text{[...]}$.","back":"The reciprocal function of sine is $\\boxed{\\operatorname{cosec}\\theta=\\frac{1}{\\sin\\theta}}$.","points":null,"mcqOptions":null},{"id":"dac553dd-be3e-4745-b57e-0ea0b9888d8b","cardType":"cloze","front":"The reciprocal function of tangent is $\\text{[...]}$.","back":"The reciprocal function of tangent is $\\boxed{\\cot\\theta=\\frac{1}{\\tan\\theta}}$.","points":null,"mcqOptions":null},{"id":"85f103da-36da-4d3b-aedd-4a479050ccef","cardType":"basic","front":"How does $\\sec\\theta$ differ from $\\cos^{-1}\\theta$?","back":"$$\\sec\\theta$ is a reciprocal; $\\cos^{-1}\\theta$ finds an angle.","points":2,"mcqOptions":null},{"id":"8b1775df-5e5a-4bfe-8782-851815bc47f6","cardType":"basic","front":"What does $\\sec^2\\theta$ mean?","back":"$$\\mathbf{(\\sec\\theta)^2}$","points":1,"mcqOptions":null},{"id":"cc682efb-e139-48e6-b48a-4a9cbb49ccba","cardType":"basic","front":"What does $\\equiv$ indicate in a trigonometric statement?","back":"Both sides are identically equal throughout their domain.","points":1,"mcqOptions":null},{"id":"234a9772-331b-4c07-aaad-ea2a887e656b","cardType":"basic","front":"Why is $\\sin\\theta=\\frac12$ an equation rather than an identity?","back":"It is true only for particular values of $\\theta$.","points":2,"mcqOptions":null},{"id":"7a5dd1fe-5e13-4296-8840-6bd7fe662f99","cardType":"cloze","front":"Tangent can be written in terms of sine and cosine as $\\text{[...]}$.","back":"Tangent can be written in terms of sine and cosine as $\\boxed{\\tan\\theta\\equiv\\frac{\\sin\\theta}{\\cos\\theta}}$.","points":null,"mcqOptions":null},{"id":"72763854-6297-4a50-b470-4deb687792ac","cardType":"basic","front":"Why is $\\tan\\theta$ undefined when $\\cos\\theta=0$?","back":"Its expression would require division by zero.","points":2,"mcqOptions":null},{"id":"b826f51b-7a6d-4346-9763-653883b957db","cardType":"basic","front":"Simplify $\\dfrac{\\sin\\theta}{\\tan\\theta}$.","back":"$$\\mathbf{\\cos\\theta}$","points":1,"mcqOptions":null},{"id":"d8cdb341-d1f7-424b-bfb0-735a30990c36","cardType":"cloze","front":"The fundamental Pythagorean identity is $\\text{[...]}$.","back":"The fundamental Pythagorean identity is $\\boxed{\\sin^2\\theta+\\cos^2\\theta\\equiv1}$.","points":null,"mcqOptions":null},{"id":"90035200-4843-4ad9-98bf-ee0c7d672307","cardType":"basic","front":"Why does $\\sin^2\\theta+\\cos^2\\theta\\equiv1$ follow from the unit circle?","back":"The coordinates $(\\cos\\theta,\\sin\\theta)$ satisfy Pythagoras with radius 1.","points":2,"mcqOptions":null},{"id":"2a3b3081-5674-4c93-acc1-2c250dabeb2a","cardType":"basic","front":"Rewrite $1-\\cos^2\\theta$ as a single trigonometric term.","back":"$$\\mathbf{\\sin^2\\theta}$","points":1,"mcqOptions":null},{"id":"3813e0b8-b660-4f09-a328-a5a8cc935b50","cardType":"basic","front":"Simplify $3\\sin^2\\theta+3\\cos^2\\theta-2\\cos^2\\theta$.","back":"$$\\mathbf{3-2\\cos^2\\theta}$","points":2,"mcqOptions":null},{"id":"9b02b9a8-3586-486e-a1b0-705b645b66ba","cardType":"basic","front":"Which identity links secant and tangent?","back":"$$\\mathbf{\\sec^2\\theta\\equiv1+\\tan^2\\theta}$","points":1,"mcqOptions":null},{"id":"c476f23c-2daf-4787-891c-cd38b945f88f","cardType":"basic","front":"How is $\\sec^2\\theta\\equiv1+\\tan^2\\theta$ derived from the fundamental identity?","back":"Divide every term by $\\cos^2\\theta$.","points":2,"mcqOptions":null},{"id":"c74edf12-bd6c-4f71-9e06-09c351f43ddd","cardType":"basic","front":"Simplify $\\dfrac{\\sec^2\\theta-1}{\\tan\\

1.8.5 Trigonometric identities Flashcards

1.8.5 Trigonometric identities Flashcards