which of these is true for the function f given by f(x)=3 sin(x/2)? a. the period is 4π. b. the period is…
which of these is true for the function f given by f(x)=3 sin(x/2)? a. the period is 4π. b. the period is 2π. c. the period is 3. d. the period is π.
Answer
Explanation:
Step1: Recall period - formula for sine function
The period of the function $y = A\sin(Bx)$ is $T=\frac{2\pi}{|B|}$.
Step2: Identify the value of B
For the function $f(x)=3\sin(\frac{x}{2})$, we have $B = \frac{1}{2}$.
Step3: Calculate the period
$T=\frac{2\pi}{\left|\frac{1}{2}\right|}=4\pi$.
Answer:
A. The period is $4\pi$.