Chapter 6: Q. 16 (page 429)

Write the equation of a sine function that has the given characteristics.
Amplitude: $3$
Period: $π$
Phase shift: $2$

Short Answer

Expert verified

The obtained equation from the given information is $y = 3 \sin 2 (x - 4)$

Step by step solution

Step 1. Find the value of ω and ϕ

We know that, $T = \frac{2 π}{ω}$

So,

Substituting $T = \frac{π}{2}$ in the above equation, we get:

$T = \frac{2 π}{ω} \frac{π}{2} = \frac{2 π}{ω} ω = 4$

We have:

$\frac{ϕ}{ω} = 2 \frac{ϕ}{4} = 2 [ω = 4] ϕ = 8$

Step 2. Writing the equation

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

Substituting $A = 3 ω = 4 ϕ = 8$ in the above equation, we get:

$y = 3 \sin (4 x - 8) y = 3 \sin 4 (x - 2)$

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Write the equation of a sine function that has the given characteristics.
Amplitude: $3$
Period: $π$
Phase shift: $2$

Short Answer

Step by step solution

Step 1. Find the value of ω and ϕ

Step 2. Writing the equation

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Write the equation of a sine function that has the given characteristics.Amplitude:3Period:πPhase shift:2

Short Answer

Step by step solution

Step 1. Find the value of ω and ϕ

Step 2. Writing the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Write the equation of a sine function that has the given characteristics.
Amplitude: $3$
Period: $π$
Phase shift: $2$