0/3 attempts next attempt points: 10? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 find the amplitude, phase shift…

Explanation:

Step1: Recall amplitude formula

For a sine - function of the form $y = A\sin(Bx - C)+D$, the amplitude is given by $|A|$. Here, $A = 3$, so the amplitude is $|3|=3$.

Step2: Recall phase - shift formula

The phase - shift of the function $y = A\sin(Bx - C)+D$ is given by $\frac{C}{B}$. Here, $B = 7$ and $C=\frac{\pi}{6}$, so the phase - shift is $\frac{\frac{\pi}{6}}{7}=\frac{\pi}{42}$.

Step3: Recall period formula

The period of the function $y = A\sin(Bx - C)+D$ is given by $\frac{2\pi}{|B|}$. Since $B = 7$, the period is $\frac{2\pi}{7}$.

Answer:

The amplitude is 3 The phase shift is $\frac{\pi}{42}$ The period is $\frac{2\pi}{7}$