find the period of this function.\ny = \\pi\\sin(\\frac{1}{4}\\theta+\\frac{\\pi}{2})

Answer:

$8$

Explanation:

Step1: Recall period formula

For $y = A\sin(Bx + C)$, the period $T=\frac{2\pi}{|B|}$.

Step2: Identify B - value

In $y=\pi\sin(\frac{1}{4}\theta+\frac{\pi}{2})$, $B = \frac{1}{4}$.

Step3: Calculate the period

$T=\frac{2\pi}{\left|\frac{1}{4}\right|}=8\pi$. Since we want the number that multiplies $\pi$ in the period, the answer is $8$.