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Q43.

Expert-verified

Algebra 2

Found in: Page 768

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

What is the period of $f (x) = \frac{1}{2} \cos (3 x)$ and then graph the function.
$(A) 120 {}^{\circ}{(B)} 180 {}^{\circ}{(C)} 360 {}^{\circ}{(D)} 720 °$

The period of $f (x) = \frac{1}{2} \cos (3 x)$ is $120 °$ . So, option (A) is correct.

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 $f (x) = \frac{1}{2} \cos (3 x)$ .

Step 2. Concept used.

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

Step 3. Evaluating period of the given function.

With the help of concept stated above, the period of the function is evaluated as:

The period of $f (x) = \frac{1}{2} \cos (3 x)$ is $\frac{360 °}{|3|} = 120 °$ .

Step 4. Conclusion.

The period of $f (x) = \frac{1}{2} \cos (3 x)$ is $120 °$ . So, option (A) is correct.

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