   # Find the period amplitude, and phase shift, and graph at least two periods of each equation: y = 15 sin ( 2 3 x − 120 ° ) ### Elementary Technical Mathematics

12th Edition
Dale Ewen
Publisher: Cengage Learning
ISBN: 9781337630580

#### Solutions

Chapter
Section ### Elementary Technical Mathematics

12th Edition
Dale Ewen
Publisher: Cengage Learning
ISBN: 9781337630580
Chapter 14.2, Problem 24E
Textbook Problem
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## Find the period amplitude, and phase shift, and graph at least two periods of each equation: y = 15 sin ( 2 3 x − 120 ° )

To determine

To calculate: The period and amplitude of the given expression y=15sin(23x120°) and graph the provided function.

### Explanation of Solution

Given Information:

The provided function is y=15sin(23x120°).

Formula Used:

For a given function y=Asct(Bx+Q), where sct=sin/cos/tan

Here, A=Amplitude, Period=360B and Phase=QB

Calculation:

Consider the provided function:

y=15sin(23x120°)

Now, compare the provided function y=15sin(23x120°) with the function y=Asct(Bx+Q).

So, it can be concluded that,

Amplitude=15

And,

period=36023=36032=540

And,

phase=12023=180

Thus, The amplitude is 15, period is 540° and phase is 180° right n the given function y=15sin(23x120).

Graph:

Consider the provided function:

y=15sin(23x120)

Now, obtain the values of y by assuming corresponding values of x as:

Substitute x=0 in the function y=15sin(23x120).

y=15cos(230120)=15cos(120)=150.5=7.5

Substitute x=30 in the function y=15sin(23x120).

y=15cos(2330120)=15cos(100)=150.1736=2.6047

Substitute x=60 in the function y=15sin(23x120).

y=15cos(2360120)=15cos(80)=150

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