I am assuming you meant y=sin(x) from 0 to 2pi? Remember that the maximum and minimum points on the sine graph will occur 1/4 and 3/4 through the cycle, or period and the zeros occur at the beginning, middle and end. So you want to find the distance 1/4 of the way to 2pi and 3/4 of the way to 2pi.
With this information, you can easily calculate your answer:)
Answer:

Step-by-step explanation:
Step one:
Given data
dimension of the rectangle
Width = 8y-1.5
Length = 1.5y+9
Required
The expression to represents the Perimeter
Step two:
the perimeter of a rectangle is expressed as

collect like terms

Slope: 1.5
Work: I used the slope formula method which is y2 - y1/ x2 - x1. After plugging it in, the new equation is 4 - (-2) / 10 - 6. After subtraction, I had gotten 6/4. And when you divide 6/4, you get 1.5
I hope this helps. :)
See, please, suggested decision:
When the line intersects the xy-plane, then parameter z=0, when does the xz - y=0 and when does yz, x=0. All the details are in attachment.
If it's possible, check arithmetic part.