4) Period of y= sin 3x
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
Help number 4 answer is 2pi/3
![**Period of Trigonometric Functions - Educational Explanation**
In this section, we will explore the concept of the period of trigonometric functions. Specifically, we will examine the period of the function \( y = \sin 3x \).
### Period of \( y = \sin 3x \)
The period of a sine function is determined by the coefficient of \( x \) in the argument of the sine function. The general formula for the period of a function \( y = \sin bx \) is:
\[
\text{Period} = \frac{2\pi}{b}
\]
For the function \( y = \sin 3x \), the coefficient \( b \) is 3. Therefore, the period of \( y = \sin 3x \) is calculated as follows:
\[
\text{Period} = \frac{2\pi}{3}
\]
This means that the function completes one full cycle every \( \frac{2\pi}{3} \) units along the x-axis.
### Graph Explanation
A graph is presented with x and y axes labeled. There are tick marks on both axes, which will help in plotting the sine wave. While the graph itself currently doesn't show the wave of \( y = \sin 3x \), you can envision the sine wave completing one cycle between 0 and \( \frac{2\pi}{3} \).
The y-axis is used for the amplitude of the function, and the x-axis is used to mark the period and oscillation of the wave.
Remember, understanding the period of trigonometric functions is crucial for analyzing wave behavior, whether in mathematics or applied sciences like physics and engineering.
**Next Topic:**
Explore the period of \( y = 2 \cos \frac{1}{2}x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3def50f-0bee-45b6-a067-ec9125eb6917%2F75d0574a-9694-41df-9512-dca5a38b55b8%2F5k8c9lf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Period of Trigonometric Functions - Educational Explanation**
In this section, we will explore the concept of the period of trigonometric functions. Specifically, we will examine the period of the function \( y = \sin 3x \).
### Period of \( y = \sin 3x \)
The period of a sine function is determined by the coefficient of \( x \) in the argument of the sine function. The general formula for the period of a function \( y = \sin bx \) is:
\[
\text{Period} = \frac{2\pi}{b}
\]
For the function \( y = \sin 3x \), the coefficient \( b \) is 3. Therefore, the period of \( y = \sin 3x \) is calculated as follows:
\[
\text{Period} = \frac{2\pi}{3}
\]
This means that the function completes one full cycle every \( \frac{2\pi}{3} \) units along the x-axis.
### Graph Explanation
A graph is presented with x and y axes labeled. There are tick marks on both axes, which will help in plotting the sine wave. While the graph itself currently doesn't show the wave of \( y = \sin 3x \), you can envision the sine wave completing one cycle between 0 and \( \frac{2\pi}{3} \).
The y-axis is used for the amplitude of the function, and the x-axis is used to mark the period and oscillation of the wave.
Remember, understanding the period of trigonometric functions is crucial for analyzing wave behavior, whether in mathematics or applied sciences like physics and engineering.
**Next Topic:**
Explore the period of \( y = 2 \cos \frac{1}{2}x \).
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