Question

find the period of this function.

\\y = \pi \sin\left(\frac{1}{10}\theta + \frac{\pi}{2}\
ight)\\

\\?\pi\\

Explanation:

⚡ Using what you learned: Amplitude, Period, Phase Shift

Step 1: Identify the coefficient of the variable

For a trigonometric function of the form \( y = a \sin(b\theta + c) \), the coefficient of \( \theta \) is \( b \):

$$ b = \frac{1}{10} $$

Step 2: Calculate the period

The formula for the period \( P \) of a sine function is:

$$ P = \frac{2\pi}{|b|} $$

Substitute \( b = \frac{1}{10} \):

$$ P = \frac{2\pi}{\frac{1}{10}} = 2\pi \cdot 10 = 20\pi $$

Answer:

20