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Q8.

Expert-verified

Algebra 2

Found in: Page 767

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the amplitude if it exists and period of the function $y = \csc (2 θ)$ and then graph the function.

The amplitude of $y = \csc (2 θ)$ is undefined.

The period of $y = \csc (2 θ)$ is $π$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given function is $y = \csc (2 θ)$ .

Step 2. Concept used.

A function of the form $y = a \csc (b x) and y = a \sec (b x)$ has undefined amplitude and period $\frac{360 °}{|b|} or \frac{2 π}{|b|}$ .

Step 3. Evaluating amplitude and period of the given function.

With the help of concept stated above, the amplitude and period of the function $y = \csc (2 θ)$ is evaluated as:

The amplitude of $y = \csc (2 θ)$ is undefined.

The period of $y = \csc (2 θ)$ is $\frac{2 π}{|2|} = π$ .

Step 4. Sketch the graph for the function.

The graph for the function $y = \csc (2 θ)$ is shown below.

Step 5. Conclusion.

The amplitude of $y = \csc (2 θ)$ is undefined.

The period of $y = \csc (2 θ)$ is $π$ .

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