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Chapter 6: Q. 35 (page 435)

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.
$y = 4 \sin (3 x)$

Short Answer

Expert verified

The amplitude, time period, phase shift is $4, \frac{2 π}{3}, 0$ respectively and the graph is

Step by step solution

01

Given information

Given function $y = 4 \sin (3 x)$

02

Comparing with y=Asinbx and calculating

Comparing, we get

$A = 4 T = \frac{2 π}{b} T = \frac{2 π}{3} \frac{ϕ}{ω} = \frac{0}{3} \frac{ϕ}{ω} = 0$

03

Sketching the graph

Sketching, we get

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Most popular questions from this chapter

Use the graph to determine the domain

and the range of function

$y = \tan (\frac{1}{4} x) + 1$

find the value of the remaining five trigonometric functions of $ϑ$

role="math" localid="1646316653225" $\cos ϑ = \frac{2}{3} \frac{3 π}{2} < ϑ < 2 π$

True or false The function $f (x) = \sqrt{x}$ is even.

find the value of the remaining five trigonometric functions of

$\tan ϑ = \frac{- 12}{5} π / 2 < ϑ < π$

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

See all solutions

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