Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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( 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 \(\frac{2\pi}{3}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65af9c16-2b1a-4650-81ff-ba0e15931f26%2F9cf87dfc-6036-4291-867c-7be535a89579%2F1yohw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## 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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