Chapter 6: Q. 8 (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.
$y = - 2 \cos (2 x - \frac{π}{2})$

Short Answer

Expert verified

Amplitude: $A = 2$

Time period: $T = π$

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 cosine function form is given as:

$y = A \cos (ω t - ϕ) + B$

Where,

$A =$ Amplitude

$\frac{2 π}{ω} =$ Time period

$\frac{ϕ}{ω} =$ Phase shift

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

$A = |- 2| = 2$

Time period,

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

Phase Shift:

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

Step 2. Graph the function

The graph 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.
$y = - 2 \cos (2 x - \frac{π}{2})$

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=-2cos2x-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

Mechanics Maths

Applied Mathematics

Pure Maths

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

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.
$y = - 2 \cos (2 x - \frac{π}{2})$