rigonometric equations Flashcards","topicId":"3bbbb9a1-6601-4e80-b5e3-15e73037c2dc","topicSlug":"solving-trigonometric-equations","cards":[{"id":"d120de1e-d4ab-4d53-ae12-9f6e88b8267f","cardType":"basic","front":"How can you identify whether an interval uses radians or degrees?","back":"$\\pi$ indicates radians; a degree symbol indicates degrees.","points":1,"mcqOptions":null},{"id":"bdc11764-62ff-4d90-8a80-f07929801f48","cardType":"cloze","front":"The period of both $\\sin x$ and $\\cos x$ is $\\text{[...]}$ radians.","back":"The period of both $\\sin x$ and $\\cos x$ is $\\boxed{2\\pi}$ radians.","points":null,"mcqOptions":null},{"id":"b3fb1c52-27e5-4392-8895-264a74b11953","cardType":"cloze","front":"The period of $\\tan x$ is $\\text{[...]}$ radians.","back":"The period of $\\tan x$ is $\\boxed{\\pi}$ radians.","points":null,"mcqOptions":null},{"id":"a285e898-af05-4efc-b890-2cb4a880475b","cardType":"basic","front":"Why can an inverse-trigonometric calculator answer be insufficient?","back":"It gives only the principal value, so symmetry may produce other solutions.","points":2,"mcqOptions":null},{"id":"9631c950-24eb-471b-bc7d-2008bb7c11da","cardType":"cloze","front":"Over one full turn, $\\sin x=\\sin\\alpha$ gives $x=\\alpha$ or $\\text{[...]}$.","back":"Over one full turn, $\\sin x=\\sin\\alpha$ gives $x=\\alpha$ or $\\boxed{x=\\pi-\\alpha}$.","points":null,"mcqOptions":null},{"id":"4d5af7c8-4ae3-416b-b2b9-4286784f808d","cardType":"cloze","front":"Over one full turn, $\\cos x=\\cos\\alpha$ gives $x=\\alpha$ or $\\text{[...]}$.","back":"Over one full turn, $\\cos x=\\cos\\alpha$ gives $x=\\alpha$ or $\\boxed{x=2\\pi-\\alpha}$.","points":null,"mcqOptions":null},{"id":"6635539d-e560-433b-a95c-77c142569c75","cardType":"cloze","front":"The solutions of $\\tan x=\\tan\\alpha$ repeat according to $\\text{[...]}$, where $n$ is an integer.","back":"The solutions of $\\tan x=\\tan\\alpha$ repeat according to $\\boxed{x=\\alpha+n\\pi}$, where $n$ is an integer.","points":null,"mcqOptions":null},{"id":"cb00aa47-3616-4037-aec8-24e46b554e4a","cardType":"basic","front":"Which algebraic values of $\\sin x$ and $\\cos x$ are possible for real $x$?","back":"Only values in $[-1,1]$.","points":1,"mcqOptions":null},{"id":"8b12a032-61dc-457d-8572-332319f2f787","cardType":"basic","front":"Why can $\\tan x=a$ have solutions for any real $a$?","back":"The range of tangent is all real numbers.","points":2,"mcqOptions":null},{"id":"7d744618-aaf7-425b-8e1d-75e1ee03cef8","cardType":"basic","front":"How should a reference angle be found when the trigonometric value is negative?","back":"Use the positive magnitude, then place it in quadrants with the required negative sign.","points":2,"mcqOptions":null},{"id":"e36fbf17-3b3e-4fed-b089-9aae368b2c20","cardType":"basic","front":"Solve $2\\sin x-1=0$ for $0\\le x<2\\pi$.","back":"$x=\\frac{\\pi}{6},\\ \\frac{5\\pi}{6}$","points":3,"mcqOptions":null},{"id":"5111a336-1714-44e2-a46c-24ebba536d1a","cardType":"basic","front":"Solve $\\cos x=-\\frac{\\sqrt3}{2}$ for $0\\le x<2\\pi$.","back":"$x=\\frac{5\\pi}{6},\\ \\frac{7\\pi}{6}$","points":3,"mcqOptions":null},{"id":"a6ea3232-ef14-4872-a79b-603acfdee3a7","cardType":"basic","front":"How is a quadratic trigonometric equation converted into an algebraic quadratic?","back":"Replace the complete trigonometric expression with one temporary variable.","points":2,"mcqOptions":null},{"id":"493915c3-09b3-40e1-b67f-06ff15dc4ad3","cardType":"basic","front":"What should happen if algebra gives $\\sin x=1.4$?","back":"Reject the root because $1.4\\notin[-1,1]$.","points":2,"mcqOptions":null},{"id":"a70901ae-0856-46c1-bad1-c4af80c51e91","cardType":"basic","front":"What branches result from $2\\sin^2x-\\sin x-1=0$?","back":"$\\si

1.8.7 Solving trigonometric equations Flashcards

1.8.7 Solving trigonometric equations Flashcards