find the amplitude, phase shift, and period of -5cos(9x - π/2) - 10. the amplitude is. the phase shift is…

Explanation:

Step1: Recall amplitude formula

For a cosine function of the form $y = A\cos(Bx - C)+D$, the amplitude is $|A|$. Given $y=-5\cos(9x - \frac{\pi}{2})-10$, here $A = - 5$. So, the amplitude is $| - 5|=5$.

Step2: Recall phase - shift formula

The phase - shift of the cosine function $y = A\cos(Bx - C)+D$ is given by $\frac{C}{B}$. Here, $B = 9$ and $C=\frac{\pi}{2}$. So, the phase - shift is $\frac{\frac{\pi}{2}}{9}=\frac{\pi}{18}$.

Step3: Recall period formula

The period of the cosine function $y = A\cos(Bx - C)+D$ is given by $\frac{2\pi}{|B|}$. Here, $B = 9$, so the period is $\frac{2\pi}{9}$.

Answer:

The amplitude is 5 The phase shift is $\frac{\pi}{18}$ The period is $\frac{2\pi}{9}$