Chapter 6: Q. 17 (page 429)

Write the equation of a sine function that has the given characteristics.
Amplitude: $3$
Period: $\frac{π}{2}$
Phase shift: $- \frac{1}{3}$

Short Answer

Expert verified

The obtained equation from the given information is $y = 3 \sin (\frac{2}{3} x + \frac{2}{9})$

Step by step solution

Step 1. Find the value of ϕ and ω

We know that, $T = \frac{2 π}{ω}$ .

So,

Substituting $T = 3 π$ in the above equation, we get:

$T = \frac{2 π}{ω} 3 π = \frac{2 π}{ω} ω = \frac{2}{3}$

We have:

$\frac{ϕ}{ω} = - \frac{1}{3} \frac{ϕ}{\frac{2}{3}} = \frac{- 1}{3} ϕ = - \frac{2}{9}$

Step 2. Find the equation

The general sine function is $y = A \sin (ω x - ϕ)$ .

Substituting the value $ω = \frac{2}{3} ϕ = \frac{- 1}{3}$ , we get:

$y = 3 \sin (\frac{2}{3} x - (\frac{2}{9})) y = 3 \sin (\frac{2}{3} x + \frac{2}{9})$

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.

Write the equation of a sine function that has the given characteristics.
Amplitude: $3$
Period: $\frac{π}{2}$
Phase shift: $- \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Find the value of ϕ and ω

Step 2. Find the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Probability and Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write the equation of a sine function that has the given characteristics.Amplitude:3Period:π2Phase shift:-13

Short Answer

Step by step solution

Step 1. Find the value of ϕ and ω

Step 2. Find the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Probability and Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write the equation of a sine function that has the given characteristics.
Amplitude: $3$
Period: $\frac{π}{2}$
Phase shift: $- \frac{1}{3}$