How do you find the amplitude, period, phase shift for $y = sin (x + \frac{π}{3})$ $y=sin(x+pi/3)$ ?

Question

4916 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-08T16:38:18

See the explanation below.

The sine function is defined for

$AA x in RR$ ,

$-1<=sinx<=1$

The amplitude $=1$

To calculate the period of a T-periodic function

Let $f(x)=sin(x+pi/3)$

$f(x)=f(x+T)$

$f(x+T)=sin(x+pi/3+T)=sin(x+pi/3)cosT+cos(x+pi/3)sinT$

$sin(x+pi/3)cosT+cos(x+pi/3)sinT=sin(x+pi/3)$

$cosT=1$ and $sinT=0$

$T=0, T=2pi$ , $[2pi]$

The period is $T=2pi$

The phase shift is $=pi/3$

graph{sin(x+pi/3) [-8.23, 17.08, -6.37, 6.29]}

How do you find the amplitude, period, phase shift for y=sin(x+pi/3)y=sin(x+π3)y=sin(x+pi/3)?