Exam 6: Trigonometric Identities and Conditional Equations

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Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What is wrong with this problem? "Find cos s if sec Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What is wrong with this problem? Find cos s if sec   and s is in quadrant III. and s is in quadrant III."

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Use a sum or difference identity to find the exact value. -sin(-15°)

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Find all real numbers in the interval Find all real numbers in the interval   that satisfy the equation. -2 sin x cos x + cos x = 0 that satisfy the equation. -2 sin x cos x + cos x = 0

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Find all real numbers that satisfy the equation. -sin x = - 22

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Use the appropriate sum or difference identity to write the given expression as a function of x alone. -sin (270° - x)

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Identify the equation as either an identity or not. -Identify the equation as either an identity or not. -

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Decide whether the expression is or is not an identity. -c Decide whether the expression is or is not an identity. -c

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For the following equation, graph For the following equation, graph   on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -(  on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -( For the following equation, graph   on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -(

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Find the exact value by using a half-angle identity. -cos Find the exact value by using a half-angle identity. -cos

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Express the given trigonometric function in terms of the indicated function. -sec Express the given trigonometric function in terms of the indicated function. -sec   in terms of cot  in terms of cot Express the given trigonometric function in terms of the indicated function. -sec   in terms of cot

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Simplify the expression. -Simplify the expression. -

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Use a sum-to-product identity to rewrite the expression. -Use a sum-to-product identity to rewrite the expression. -

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Solve the problem. -Consider the formula T = 591 - 76 cos Solve the problem. -Consider the formula T = 591 - 76 cos   is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of   for which the value of T will be 607? is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of Solve the problem. -Consider the formula T = 591 - 76 cos   is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of   for which the value of T will be 607? for which the value of T will be 607?

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Find all real numbers that satisfy the equation. -sin x = Find all real numbers that satisfy the equation. -sin x =

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Use a product-to-sum identity to rewrite the expression. -cos 20° sin 45°

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Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. -Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. -  + 8 sin x - 4 = 0 + 8 sin x - 4 = 0

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Find the exact value using a double-angle identity. -sin(300°)

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Use a half-angle identity to find an exact value for the following, given the information about x. -Find tan Use a half-angle identity to find an exact value for the following, given the information about x. -Find tan   , given that sin x = -   and 270° < x < 360°. , given that sin x = - Use a half-angle identity to find an exact value for the following, given the information about x. -Find tan   , given that sin x = -   and 270° < x < 360°. and 270° < x < 360°.

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Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. -sin 2x = csc 2x

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Use an identity to find the exact value of the expression. -Use an identity to find the exact value of the expression. -

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