Question

1. find the period of $y = 2\sin(5x)$.

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

b) $\frac{2\pi}{3}$

c) $10\pi$

d) $5$

Explanation:

Step1: Recall period formula for $\sin(Bx)$

The period of $y = A\sin(Bx)$ is $\frac{2\pi}{|B|}$.

Step2: Identify $B$ from given function

For $y=2\sin(5x)$, $B=5$.

Step3: Calculate period

$\text{Period} = \frac{2\pi}{5}$

Answer:

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