Answer
$y= 7+2 \cos (\dfrac{4}{5}) (x-\dfrac{ 3\pi}{4}) $
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, $|a|= \dfrac{M-m}{2}= \dfrac{9-5}{2}= \dfrac{4}{2}$
Thus, we have $|a|=2$
Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{9+5}{2}$
This gives: $|k|=7$
Therefore, the period is: $P=2(2 \pi- \dfrac{ 3\pi}{4}) =\dfrac{5\pi}{2}$
and $\dfrac{2 \pi}{a}=\dfrac{ 5\pi}{2} \implies a=\dfrac{4}{5}$
Here, the phase difference is: $\dfrac{ 3\pi}{4}$
Hence, the function is: $y= 7+2 \cos (\dfrac{4}{5}) (x-\dfrac{ 3\pi}{4}) $
