what is the period of $y = 7sinleft(-\frac{3pi}{4}x-\frac{pi}{4}\right)+6$? give an exact value.

Explanation:

Step1: Recall period formula

For $y = A\sin(Bx - C)+D$, the period $T=\frac{2\pi}{|B|}$.

Step2: Identify B value

In $y = 7\sin(-\frac{3\pi}{4}x-\frac{\pi}{4}) + 6$, $B =-\frac{3\pi}{4}$.

Step3: Calculate the period

$T=\frac{2\pi}{\left|-\frac{3\pi}{4}\right|}=\frac{2\pi}{\frac{3\pi}{4}}=\frac{8}{3}$.

Answer:

$\frac{8}{3}$