Chapter 6: Q. 18 (page 429)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Find the value of ω and ϕ

We know that, $T = \frac{2 π}{ω}$

So,

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

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

We have:

$\frac{ϕ}{ω} = - 2 \frac{ϕ}{2} = - 2 ϕ = - 4$

Step 2. Find the equation

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

Substituting the value $ω = 2 ϕ = - 4 A = 2$ in the general sine function, we get:

role="math" localid="1646391977430" $y = 2 \sin (2 x - (- 4)) y = 2 \sin (2 x + 4)$

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

Short Answer

Step by step solution

Step 1. Find the value of ω and ϕ

Step 2. Find the equation

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

Short Answer

Step by step solution

Step 1. Find the value of ω and ϕ

Step 2. Find the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

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