How to Find the Period of a Sine Function

Step-by-step solution

1. Match the function to the form y = sin(bx).

   $$b = 3$$

   Why: The number in front of x is b.

2. Write the period formula.

   $$T = \frac{2\pi}{b}$$

   Why: The period is one full repeat of the wave.

3. Substitute b and simplify.

   $$T = \frac{2\pi}{3}$$

   Why: A larger b makes the wave repeat faster and the period shorter.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $y = \sin(2x)$

   Show answer

   $\pi$

2. 2

   $y = \sin(4x)$

   Show answer

   $\frac{\pi}{2}$

3. 3

   $y = \sin\left(\frac{x}{2}\right)$

   Show answer

   $4\pi$

4. 4

   $y = \sin(5x)$

   Show answer

   $\frac{2\pi}{5}$

5. 5

   $y = \cos(2x)$

   Show answer

   $\pi$