Answer
$y= 4 \cos x$
Work Step by Step
General solution for Trigonometric functions $sine$ and $cosine$ that model a sinusoid is as follows: $y=A \sin B (x-h) +k $ and $y=A \cos B (x-h)+k$
Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{4-(-4)}{2}= \dfrac{8}{2}$
Thus, we have $|a|=4$
Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{4-4}{2}$
This gives: $|k|=0$
Therefore, the period is: $P=2( \pi-0) =2 \pi$
and $\dfrac{2 \pi}{a}=2 \pi \implies a=1$
Hence, the function is: $y= 4 \cos x$
