The three zigzag functions

You will write the three composite functions of the lesson without calling the inverse functions. You will use only the pieces of the rule. The checker compares your functions with asin(sin(x)), acos(cos(x)) and atan(tan(x)).

The idea. The sine repeats every $2\pi$, so first reduce $x$ to a number $y$ between $-\pi$ and $\pi$. If $y$ is above $\dfrac{\pi}{2}$ the result is $\pi - y$, and if $y$ is below $-\dfrac{\pi}{2}$ the result is $-\pi - y$. The tangent repeats every $\pi$, so reduce $x$ to a number between $-\dfrac{\pi}{2}$ and $\dfrac{\pi}{2}$.

Your tasks.

1. Finish sin_inv_sin(x). Reduce with y = x - 2 * pi * round(x / (2 * pi)), then apply the three cases.
2. Finish cos_inv_cos(x). Reduce with y = x % (2 * pi). If y is above pi return 2 * pi - y, otherwise return y.
3. Finish tan_inv_tan(x). Return x - pi * round(x / pi).