https://file.aiquickdraw.com/mathbot/file/1727796293490tlzjsydy.jpg

The function given in the image is:

\[
y = \sin\left(\frac{1}{6}x\right)
\]

To find the period of this sine function, recall that the general form of a sine function is:

\[
y = \sin(Bx)
\]

The period of a sine function is calculated as:

\[
\text{Period} = \frac{2\pi}{|B|}
\]

In this case, \( B = \frac{1}{6} \), so the period becomes:

\[
\text{Period} = \frac{2\pi}{\frac{1}{6}} = 2\pi \times 6 = 12\pi
\]

Thus, the period of the function \( y = \sin\left(\frac{1}{6}x\right) \) is \( 12\pi \).

Would you like a more detailed explanation or have any questions?

Here are five related questions for further practice:
1. What is the period of \( y = \sin\left(\frac{1}{3}x\right) \)?
2. How does changing the coefficient inside the sine function affect the graph?
3. What is the period of \( y = \sin(2x) \)?
4. What is the amplitude of \( y = \sin\left(\frac{1}{6}x\right) \)?
5. How do you graph a sine function with a horizontal stretch?

**Tip**: The period of a sine function is always \( \frac{2\pi}{B} \), where \( B \) is the coefficient of \( x \) inside the sine function.

What is the period of the function y = sin(1/6 * x)?

Learn how to find the period of the sine function y = sin(1/6 * x). This step-by-step solution explains the formula to calculate the period for trigonometric functions, using 2π / B. Ideal for students in Grades 10-12.

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