# What is the amplitude, period and the phase shift of  f(x)= 3sin(2x + pi)?

Apr 21, 2017

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

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{sine function}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a \sin \left(b x + c\right) + d} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where amplitude "=|a|," period } = \frac{2 \pi}{b}$

$\text{phase shift "=-c/b" and vertical shift } = d$

$\text{here } a = 3 , b = 2 , c = \pi , d = 0$

$\text{amplitude " =|3|=3," period } = \frac{2 \pi}{2} = \pi$

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

Apr 21, 2017

The amplitude is $A = 3$
The period is $= \pi$
The phase shift is $= - \frac{\pi}{2}$

#### Explanation:

$y = A \sin \left(B x + C\right) + D$

Amplitude is $A$

Period is (2π)/B

Phase shift is −C/B

Vertical shift is $D$

Here, we have

y=3sin(2x+pi))

$y = 3 \sin \left(2 x + \pi\right)$

The amplitude is $A = 3$

The period is $= \frac{2 \pi}{B} = \frac{2 \pi}{2} = \pi$

The phase shift is $= - \frac{\pi}{2}$

graph{3sin(2x+pi) [-5.546, 5.55, -2.773, 2.774]}