Chapter 6: Q. 13 (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.
$y = - 3 \sin (- 2 x + \frac{π}{2})$

Short Answer

Expert verified

Amplitude, $A = 3$

Time period, $T = - 1$

Phase shift $= \frac{π}{4}$

The graph is given as:

Step by step solution

Step 1. Find the amplitude, period, and phase shift.

The general sine function form is given as:

$y = A \sin (ω t - ϕ) + B$

Where,

$A =$ Amplitude

$\frac{2 π}{ω} =$ Time period

localid="1646385012543" $\frac{ϕ}{ω} =$ Phase shift

Comparing the given function with the general function, we get:

Amplitude:

$A = |- 3| A = 3$

Time period:

$T = \frac{2 π}{ω} T = \frac{2 π}{- 2} T = - 1$

Phase shift:

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

Step 2. Graph the function

The graph of the function is given as:

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

Short Answer

Step by step solution

Step 1. Find the amplitude, period, and phase shift.

Step 2. Graph the 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=-3sin-2x+π2

Short Answer

Step by step solution

Step 1. Find the amplitude, period, and phase shift.

Step 2. Graph the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Probability and Statistics

Discrete Mathematics

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