Question

A cosine function has a period of {3\pi }{4}" alt="\frac{3\pi }{4}" align="absmiddle" class="latex-formula"> , an amplitude of 4, and a vertical translation 3 units down. The function is not reflected over the x-axis.
What is the equation of the cosine function?

Answer 1

Answer:

$y = 4 \cos( \frac{8}{3}x ) - 3$

Step-by-step explanation:

Based on the description, the Cosine function is of the form;

$y = a \cos \: bx + c$

Where |a| is the amplitude. We have that the amplitude is 4 so a=4.

The period is given as

$\frac{3\pi}{4}$

This can help us find the b-value.

$\frac{2\pi}{b} = \frac{3\pi}{4} \\ \implies \: b = \frac{8}{3}$

The vertical translation is 3 units down so c=-3.

Hence the equation is

$y = 4 \cos( \frac{8}{3}x ) - 3$