Question

what is the amplitude of $y = \frac{1}{2} \sin 2x$?

a. $\frac{1}{2}$

b. $\left( \frac{3\pi}{2}, 0 \
ight)$

c. $1$

d. $2$

Explanation:

Step1: Recall the amplitude formula

For a sine function in the form \( y = A\sin(Bx) \), the amplitude is the absolute value of \( A \), i.e., \( |A| \).

Step2: Identify \( A \) in the given function

In the function \( y=\frac{1}{2}\sin 2x \), we can see that \( A = \frac{1}{2} \).

Step3: Calculate the amplitude

Using the amplitude formula, the amplitude is \( |\frac{1}{2}|=\frac{1}{2} \).

Answer:

A. \(\frac{1}{2}\)