determine the amplitude, period, and phase shift (if any) of the given function. graph the function. y = sin…

determine the amplitude, period, and phase shift (if any) of the given function. graph the function. y = sin x+3 what is the amplitude of y = sin x+3? 1 (simplify your answer. type an exact answer, using π as needed.) what is the period of y = sin x+3? (simplify your answer. type an exact answer, using π as needed.)

determine the amplitude, period, and phase shift (if any) of the given function. graph the function. y = sin x+3 what is the amplitude of y = sin x+3? 1 (simplify your answer. type an exact answer, using π as needed.) what is the period of y = sin x+3? (simplify your answer. type an exact answer, using π as needed.)

Answer

Explanation:

Step1: Recall period - formula for sine function

The general form of a sine function is $y = A\sin(Bx - C)+D$. For the function $y=\sin x + 3$, we have $A = 1$, $B = 1$, $C = 0$, and $D=3$. The period of a sine - function $y = A\sin(Bx - C)+D$ is given by the formula $T=\frac{2\pi}{|B|}$.

Step2: Calculate the period

Since $B = 1$, substituting $B$ into the period formula $T=\frac{2\pi}{|B|}$, we get $T=\frac{2\pi}{|1|}=2\pi$.

Answer:

$2\pi$