find the period of this function.\ny = \\pi\\sin(\\frac{1}{10}\\theta+\\frac{\\pi}{2})

Explanation:

Step1: Recall sine - function period formula

For a sine function of the form $y = A\sin(Bx + C)$, the period $T$ is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

In the function $y=\pi\sin(\frac{1}{10}\theta+\frac{\pi}{2})$, we have $B = \frac{1}{10}$.

Step3: Calculate the period

Substitute $B=\frac{1}{10}$ into the period formula $T=\frac{2\pi}{|B|}$. So $T=\frac{2\pi}{\frac{1}{10}}=20\pi$.

Answer:

$20$