Answer
$y = 3-4~sin~(\frac{5}{2}x+\pi)$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0af5aae0-064d-4d47-981f-322a2d6bcba4/result_image/1531375422.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015227Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=97799431070bb9fddcffb48ade1f21958d81483825eb780d80fe759774407b17)
Work Step by Step
$y = 3-4~sin~(\frac{5}{2}x+\pi)$
When $x = 0$, then $y = 3-4~sin~\pi = 3$
When $x = \frac{\pi}{5}$, then $y = 3-4~sin~\frac{3\pi}{2} = 7$
When $x = \frac{2\pi}{5}$, then $y = 3-4~sin~2\pi= 3$
When $x = \frac{3\pi}{5}$, then $y = 3-4~sin~\frac{5\pi}{2} = -1$
When $x = \frac{4\pi}{5}$, then $y = 3-4~sin~3\pi = 3$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0af5aae0-064d-4d47-981f-322a2d6bcba4/steps_image/small_1531375422.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015227Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=42646a75adf891d0ee82a299c11da693cb8798be7f781bd2c725fe9da246612b)