Answer
$y= 1 - 7\cos 6x$
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, $|a|= \dfrac{M-m}{2}= \dfrac{8-(-6)}{2}= \dfrac{14}{2}$
Thus, we have $|a|=7$
Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{8+(-6)}{2}$
This gives: $|k|=1$
Therefore, the period is: $P=2( \dfrac{\pi}{6}-0) =\dfrac{\pi}{3}$
and $\dfrac{2 \pi}{a}=\dfrac{\pi}{3} \implies a=6$
Hence, the function is: $y= 1 - 7\cos 6x$
