homework #15 - phase shift and modeling score: 8.53/39 answered: 7/14 question 3 score on last try: 1.2 of 2…

Explanation:

Step1: Recall amplitude formula

For $y = A\sin(Bx - C)+D$, amplitude is $|A|$. Here $A = 6$, so amplitude is $6$.

Step2: Recall period formula

The period of $y=\sin(Bx - C)+D$ is $T=\frac{2\pi}{|B|}$. Given $B=\frac{7\pi}{4}$, then $T = \frac{2\pi}{\frac{7\pi}{4}}=\frac{8}{7}$.

Step3: Recall horizontal - shift formula

For $y = A\sin(Bx - C)+D$, horizontal shift is $\frac{C}{B}$. Rewrite $y = 6\sin(\frac{7\pi}{4}x+7\pi)$ as $y = 6\sin(\frac{7\pi}{4}(x + 4))$. So horizontal shift is $4$ units to the left.

Step4: Recall mid - line formula

For $y = A\sin(Bx - C)+D$, mid - line is $y = D$. Here $D = 8$, so mid - line is $y = 8$.

Answer:

The period is $\frac{8}{7}$, the horizontal shift is $4$ units to the left.