( 15 ) Question is in the photo below ## Exercise: Finding the Period of a Trigonometric Function### Problem Statement15. Find the period of the function $ y = 5 \cos(3x) $.### Multiple Choice Options- $\frac{3\pi}{5}$- $3\pi$- $\frac{2\pi}{5}$- $\frac{2\pi}{3}$### Solution ExplanationTo find the period of a cosine function of the form $ y = A \cos(Bx) $, we use the formula for the period $ T $:\[ T = \frac{2\pi}{B} \]For the given function $ y = 5 \cos(3x) $, the coefficient of $ x $, which is $ B $, is 3. Substituting $ B $ into the formula, we get:\[ T = \frac{2\pi}{3} \]Therefore, the period of the function $ y = 5 \cos(3x) $ is $\frac{2\pi}{3}$.The correct answer is $\frac{2\pi}{3}$.

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Answered: 15. Find the period of the function y =…

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Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

( 15 ) Question is in the photo below

## Exercise: Finding the Period of a Trigonometric Function

### Problem Statement

15. Find the period of the function $ y = 5 \cos(3x) $.

### Multiple Choice Options
- $\frac{3\pi}{5}$
- $3\pi$
- $\frac{2\pi}{5}$
- $\frac{2\pi}{3}$

### Solution Explanation

To find the period of a cosine function of the form $ y = A \cos(Bx) $, we use the formula for the period $ T $:

\[ T = \frac{2\pi}{B} \]

For the given function $ y = 5 \cos(3x) $, the coefficient of $ x $, which is $ B $, is 3. Substituting $ B $ into the formula, we get:

\[ T = \frac{2\pi}{3} \]

Therefore, the period of the function $ y = 5 \cos(3x) $ is $\frac{2\pi}{3}$.

The correct answer is $\frac{2\pi}{3}$.

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