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

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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]}