Answer
$y = -4~sin~x$
We can see the graph below.
The period is $2\pi$.
The amplitude is 4.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/4434611f-4cfc-4591-9faa-cc55b6cfd8ab/result_image/1531237524.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T014447Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=4ca2c3814f91aeadec283fc88dcf021617871d6b0161b498319af5023939f691)
Work Step by Step
$y = -4~sin~x$
When $x = 0$, then $y = -4~sin~0 = 0$
When $x = \frac{\pi}{2}$, then $y = -4~sin~\frac{\pi}{2} = -4$
When $x = \pi$, then $y = -4~sin~\pi = 0$
When $x = \frac{3\pi}{2}$, then $y = -4~sin~\frac{3\pi}{2} = 4$
When $x = 2\pi$, then $y = -4~sin~2\pi = 0$
We can see the graph below.
The period is $2\pi$
The amplitude is 4
![](https://gradesaver.s3.amazonaws.com/uploads/solution/4434611f-4cfc-4591-9faa-cc55b6cfd8ab/steps_image/small_1531237524.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T014447Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=ab9e25b07f1984b44ff83ff1bd16d774d1d5f70eedffab8a01e204364bcc75ea)