## Algebra 2 (1st Edition)

$y= 1 - 7\cos 6x$
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: $y= 1 - 7\cos 6x$