Chapter 6: Q. 37 (page 435)

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.
$y = \frac{1}{2} \sin (\frac{3}{2} x - π)$

Short Answer

Expert verified

The amplitude, time period , phase shift is $\frac{1}{2}, \frac{4 π}{3}, \frac{2 π}{3}$ respectively and the graph is

Step by step solution

Given information

Given function $y = \frac{1}{2} \sin (\frac{3}{2} x - π)$

Comparing with y=Asin(bx-∅)+B and calculating

Comparing, we get

$A = \frac{1}{2} T = \frac{2 π}{\frac{3}{2}} T = \frac{4 π}{3}$

The phase shift is $\frac{ϕ}{ω} = \frac{π}{\frac{3}{2}} \frac{ϕ}{ω} = \frac{2 π}{3}$

Sketching the graph

The graph is

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.
$y = \frac{1}{2} \sin (\frac{3}{2} x - π)$

Short Answer

Step by step solution

Given information

Comparing with y=Asin(bx-∅)+B and calculating

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.y=12sin32x-π

Short Answer

Step by step solution

Given information

Comparing with y=Asin(bx-∅)+B and calculating

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.
$y = \frac{1}{2} \sin (\frac{3}{2} x - π)$