Chapter 6: Q. 3 (page 429)

find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.
$y = 4 \sin (2 x - π)$

Short Answer

Expert verified

For the function $y = 4 \sin (2 x - π)$

Amplitude $A = 4$

Period $T = π$

Phase shift $\frac{ϕ}{ω} = \frac{π}{2}$

and graph of the function is

Step by step solution

Step 1. Given data

The given function is

$y = 4 \sin (2 x - π)$

Step 2. Constants of the function

Compare the function $y = 4 \sin (2 x - π)$ with general sine function form

$y = A \sin (ω x - ϕ) + b y = 4 \sin (2 x - π) + 0$

so Amplitude

$A = | 4 | A = 4$

Period

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

Phase shift

$\frac{ϕ}{ω} = \frac{π}{2}$

Step 3. Graph of function

Plot the graph of the function $y = 4 \sin (2 x - π)$

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find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.
$y = 4 \sin (2 x - π)$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Constants of the function

Step 3. Graph of function

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find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y=4sin(2x-π)

Short Answer

Step by step solution

Step 1. Given data

Step 2. Constants of the function

Step 3. Graph of function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.
$y = 4 \sin (2 x - π)$