The answer in the book shows me a graph that's a sine wave but it fluctuates twice as fast.

How????

How can y be the sine of x? The sine of x requires y to calculate, how? That's a recursive definition

What even is x? Any value? Only some values?

The sine of 2 * 0 is 0, how can both x and y be 0? Then the cosine would also be 0, they can't both be 0, or the addition of their squares will not equal 1.