find the amplitude, period, and horizontal shift of the function.\n\n$y = \\cos(x - \\frac{\\pi}{2})$…

Explanation:

Step1: Recall amplitude formula

For $y = A\cos(Bx - C)+D$, amplitude is $|A|$. In $y=\cos(x - \frac{\pi}{2})$, $A = 1$, so amplitude is $|1|=1$.

Step2: Recall period formula

The period of $y = A\cos(Bx - C)+D$ is $T=\frac{2\pi}{|B|}$. Here $B = 1$, so $T=\frac{2\pi}{|1|}=2\pi$.

Step3: Recall horizontal - shift formula

The horizontal shift of $y = A\cos(Bx - C)+D$ is $\frac{C}{B}$. Here $C=\frac{\pi}{2}$ and $B = 1$, so horizontal shift is $\frac{\frac{\pi}{2}}{1}=\frac{\pi}{2}$.

Answer:

amplitude: $1$ period: $2\pi$ horizontal shift: $\frac{\pi}{2}$