AP®MathsCollege BoardPrecalculusExam QuestionsTrigonometric & Polar FunctionsInverse & Reciprocal Trigonometric Functions

Inverse & Reciprocal Trigonometric Functions (College Board AP® Precalculus): Exam Questions

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Inverse & Reciprocal Trigonometric Functions

1
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2 marks

The function h is given by h left parenthesis x right parenthesis equals cot x.

State whether h is strictly increasing or strictly decreasing on the open interval left parenthesis 0 comma pi right parenthesis. Give a reason for your answer.

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2
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2 marks

The function m is given by m left parenthesis x right parenthesis equals sin left parenthesis arctan x right parenthesis.

Determine the exact value of m left parenthesis 1 right parenthesis. Show the work that leads to your answer.

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3
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2 marks

The function space f is given by space f left parenthesis x right parenthesis equals 3 arcsin open parentheses x over 2 close parentheses.

Determine the domain and the range of space f. Give a mathematical rationale for both based on the domain and range of the parent function space y equals arcsin x.

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4
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2 marks

The function g is given by g left parenthesis x right parenthesis equals negative 2 sec x.

(i) State the range of g.

(ii) Determine whether the point left parenthesis 0 comma negative 2 right parenthesis is a local minimum or a local maximum of g. Give a reason for your answer based on the behavior of the cosine function.

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5
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2 marks

The function g is given by g left parenthesis x right parenthesis equals negative 2 sin left parenthesis x right parenthesis.

State a restricted domain for g on which the inverse function of g can be defined. Give a reason for your answer.

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6
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2 marks

The function space p is given by space p left parenthesis x right parenthesis equals 3 csc left parenthesis 2 x right parenthesis.

Find all vertical asymptotes of the graph of space p on the interval left parenthesis 0 comma pi right parenthesis. Give a reason for your answer.

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