Homework Help is Here – Start Your Trial Now!
Math
Algebra
A wave is modeled with the function y=sin (30), where is in radians. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis.

A wave is modeled with the function y=sin (30), where is in radians. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis.

Algebra and Trigonometry (6th Edition)
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,...
See similar textbooks
icon
Related questions
Question
**Wave Function Analysis** A wave is modeled with the function \( y = \frac{1}{2} \sin(3\Theta) \), where \( \Theta \) is in radians. To understand the behavior of this wave, we will analyze its period, amplitude, and points of intersection with the x-axis. ### Amplitude The amplitude of a sine function \( y = A \sin(B\Theta) \) is given by the coefficient \( A \). In this case, \( A = \frac{1}{2} \). This means the maximum value of the function is \( \frac{1}{2} \) and the minimum value is \( -\frac{1}{2} \). Therefore, the amplitude of the wave is \( \frac{1}{2} \). ### Period The period of a sine function \( y = A \sin(B\Theta) \) is determined by the coefficient \( B \) and is calculated using the formula \( \frac{2\pi}{B} \). Here, \( B = 3 \), so the period is \( \frac{2\pi}{3} \). This means that the wave completes one full cycle every \( \frac{2\pi}{3} \) units along the \( \Theta \)-axis. ### Points of Intersection with the X-axis The points of intersection with the x-axis (where \( y = 0 \)) occur at the zeros of the sine function. The sine function \( \sin(3\Theta) \) equals zero whenever \( 3\Theta = k\pi \) for any integer \( k \). Solving for \( \Theta \), we get \( \Theta = \frac{k\pi}{3} \). Hence, the wave intersects the x-axis at \( \Theta = 0, \pm \frac{\pi}{3}, \pm \frac{2\pi}{3}, \pm \pi, \ldots \).
Transcribed Image Text:**Wave Function Analysis** A wave is modeled with the function \( y = \frac{1}{2} \sin(3\Theta) \), where \( \Theta \) is in radians. To understand the behavior of this wave, we will analyze its period, amplitude, and points of intersection with the x-axis. ### Amplitude The amplitude of a sine function \( y = A \sin(B\Theta) \) is given by the coefficient \( A \). In this case, \( A = \frac{1}{2} \). This means the maximum value of the function is \( \frac{1}{2} \) and the minimum value is \( -\frac{1}{2} \). Therefore, the amplitude of the wave is \( \frac{1}{2} \). ### Period The period of a sine function \( y = A \sin(B\Theta) \) is determined by the coefficient \( B \) and is calculated using the formula \( \frac{2\pi}{B} \). Here, \( B = 3 \), so the period is \( \frac{2\pi}{3} \). This means that the wave completes one full cycle every \( \frac{2\pi}{3} \) units along the \( \Theta \)-axis. ### Points of Intersection with the X-axis The points of intersection with the x-axis (where \( y = 0 \)) occur at the zeros of the sine function. The sine function \( \sin(3\Theta) \) equals zero whenever \( 3\Theta = k\pi \) for any integer \( k \). Solving for \( \Theta \), we get \( \Theta = \frac{k\pi}{3} \). Hence, the wave intersects the x-axis at \( \Theta = 0, \pm \frac{\pi}{3}, \pm \frac{2\pi}{3}, \pm \pi, \ldots \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS