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
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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4
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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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5
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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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6
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1 mark

Find the exact value of sin open parentheses fraction numerator 7 pi over denominator 12 end fraction close parentheses.

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7
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1 mark

Find all values of x in the interval open square brackets 0 comma 2 pi close square brackets for which cos x less or equal than negative 1 half.

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8
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1 mark

Find all values of x in the interval open square brackets 0 comma 2 pi close square brackets for which cos squared x minus sin squared x equals 1.

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9
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1 mark

The function h is given by

h open parentheses x close parentheses equals fraction numerator 1 minus cos squared x over denominator sin x end fraction

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

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10
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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.

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11
1 mark

The function k is given by k left parenthesis x right parenthesis equals fraction numerator csc squared x minus 1 over denominator cos x times csc x end fraction

Rewrite k left parenthesis x right parenthesis as an expression in which cot x appears exactly once and no other trigonometric functions are involved. Show the work that leads to your answer.

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12
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2 marks

The function space p is given by space p open parentheses x close parentheses equals 2 sec squared x minus 4.

Solve space p open parentheses x close parentheses equals 0 for values of x in the interval open square brackets 0 comma 2 pi close parentheses. Show the computations that lead to your answer.

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13
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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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14
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1 mark

The function h is given by h \left(x\right) = 2 \arccos \left(3x\right).

Solve h open parentheses x close parentheses equals fraction numerator 2 pi over denominator 3 end fraction for values of x in the domain of h. Show the computations that lead to your answer.

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15
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1 mark

The function space j is given by space j open parentheses x close parentheses equals 2 open parentheses sin x close parentheses open parentheses cos x close parentheses minus sin x.

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

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16
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2 marks

The function m is given by m open parentheses x close parentheses equals sin open parentheses 2 x close parentheses plus 3. Find all input values in the domain of m that yield an output value of 7 over 2.

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17
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2 marks

Find all values of x in the interval open square brackets 0 comma 2 pi close square brackets for which sin open parentheses 2 x close parentheses equals sin open parentheses x close parentheses.

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