Answer
$y=\cos \left(2x+2\pi\right)-\frac{3}{2}$
Work Step by Step
The cosine function is:
$$y=a\cos (bx-c)+d$$
Rewriting the equation:
$$y=a\cos b\left(x-\frac{c}{b}\right)+d$$
Finding $b$:
$$period=\frac{2\pi}{b}$$ $$b=\frac{2\pi}{period}=\frac{2\pi}{\pi}=2$$
With left phase shift of $\pi$ or phase shift of $-\pi$:
$$\frac{c}{b}=-\pi$$ $$c=-\pi b=-\pi(2)=-2\pi$$
Substituting $a=1,~b=2,~c=-2\pi$ and $d=-\frac{3}{2}$, the function is:
$$y=\cos \left(2x-\left(-2\pi\right)\right)+\left(-\frac{3}{2}\right)$$ $$y=\cos \left(2x+2\pi\right)-\frac{3}{2}$$
