Question

Find the amplitude and period of f(t)=1/2sin 3t

Answer 1

Answer: Option A

The Amplitude is

$A = \frac{1}{2}$

Then the period is

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

Step-by-step explanation:

The general sine function has the following form  

$y = Asin(bx) + k$

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

$\frac{2\pi}{b}$ is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

In this case we have the following function

$f(t)=\frac{1}{2}sin(3t)$

Thus:

$b=3$

Then the period is

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

The Amplitude is

$A = \frac{1}{2}$

The answer is Option A