why does the graph of y=cos x have a rotation button and not y=sin x?

Answer 1

Because cos x is an even function and sin x is not
here is how we define even function
f(x) = f(-x)
For example Cos (30) = Cos (-30)
This does not happen with sin x, which makes it an odd function

Answer 2

When Munir B. says that cos x is an even function, he basically means that it's symmetrical over the y-axis. Odd functions are symmetrical over the origin; this shows that sin x is an odd function. However, I don't know what you mean when you say that the graph has a rotation button. What are you graphing these functions on?