determine the amplitude, period, and phase shift of the function. graph the function. y = sin(x - π/2) the…

determine the amplitude, period, and phase shift of the function. graph the function. y = sin(x - π/2) the amplitude is 1. (simplify your answer.) the period is 2π. (type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) the phase shift is (type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

determine the amplitude, period, and phase shift of the function. graph the function. y = sin(x - π/2) the amplitude is 1. (simplify your answer.) the period is 2π. (type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) the phase shift is (type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall general sine - function form

The general form of a sine function is $y = A\sin(B(x - C))+D$. For the function $y=\sin(x-\frac{\pi}{2})$, we have $A = 1$, $B = 1$, $C=\frac{\pi}{2}$ and $D = 0$.

Step2: Determine phase - shift formula

The phase - shift of the sine function $y = A\sin(B(x - C))+D$ is given by $C$.

Step3: Identify phase - shift value

Since $C=\frac{\pi}{2}$ in the function $y=\sin(x - \frac{\pi}{2})$, the phase - shift is $\frac{\pi}{2}$.

Answer:

$\frac{\pi}{2}$