AP®MathsCollege BoardPrecalculusExam QuestionsTrigonometric & Polar FunctionsTrigonometric Equations, Inequalities & Identities

Trigonometric Equations, Inequalities & Identities (College Board AP® Precalculus): Exam Questions

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Trigonometric Equations, Inequalities & Identities

1
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1 mark

The function h is given by h open parentheses x close parentheses equals 4 cos squared x.

Solve h open parentheses x close parentheses equals 3 for values of x in the interval open square brackets 0 comma space pi over 2 close parentheses.

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2
1 mark

The function k is given by space k open parentheses x close parentheses equals fraction numerator 6 over denominator tan x open parentheses csc squared x minus 1 close parentheses end fraction.

Rewrite k open parentheses x close parentheses as an expression in which tan x appears exactly once and no other trigonometric functions are involved.

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3
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1 mark

The function h is given by space h open parentheses x close parentheses equals arcsin open parentheses x over 2 close parentheses.

Solve h open parentheses x close parentheses equals pi over 4 for values of x in the domain of h.

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4
1 mark

The function k is given by space k open parentheses x close parentheses equals open parentheses fraction numerator 1 minus sin squared x over denominator sin x end fraction close parentheses sec x.

Rewrite k open parentheses x close parentheses as a single term involving tan x.

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5
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2 marks

The function m is given by

m open parentheses x close parentheses equals cos to the power of negative 1 end exponent open parentheses tan open parentheses 2 x close parentheses close parentheses.

Find all values in the domain of m that yield an output value of 0.

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6
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1 mark

The function h is given by h open parentheses x close parentheses equals 2 arctan open parentheses x close parentheses.

Solve h open parentheses x close parentheses equals pi over 2 for values of x in the domain of h.

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7
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1 mark

The function k is given by k open parentheses x close parentheses equals open parentheses 2 plus 2 tan squared x close parentheses cos space x.

Rewrite k open parentheses x close parentheses as an expression in which sec space x appears exactly once and no other trigonometric functions are involved.

How did you do?