Question

What are the amplitude, period, and phase shift of the given function? f(t)=-1/2sin(3t-2pi)

Answer 1

Answer:

The $amplitude=|A|=\frac{1}{2}$, $period=3$ and $\text{phase shift}=\frac{2\pi}{3}$.

Step-by-step explanation:

The given function is

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

The general form of sine function is

$F(t)=A\sin (Bt-C)+D$                 ....(2)

where, |A| is the amplitude, B is period, D is the vertical shift (up or down), and C/B is used to find the phase shift.

On comparing (1) and (2), we get

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

$B=3$

$C=2\pi$

$D=0$

So,

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

$period=3$

$\text{phase shift}=\frac{2\pi}{3}$

Therefore $amplitude=|A|=\frac{1}{2}$, $period=3$ and $\text{phase shift}=\frac{2\pi}{3}$.