How do you translate the graph of #y=sin(x-pi/3) #?

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Answer 1 · 2018-07-25T07:01:58

Below

#y=sin(x-pi/3)# is your #y=sinx# graph but shifted to the right by #pi/3# units

#y=asin(nx+b)# is the general form
#a# is the amplitude
#n# is used to find the period of the function
#b# is the shift to left or right

Therefore, wtih reference to the general form, #y=sin(x-pi/3# has an amplitude of 1, a shift to the right by #pi/3# units.

The period is found using this equation
#T=(2pi)/n#
#T=(2pi)/1#
#T=2pi#
That means the graph finishes one cycle in #2pi#

Below is #y=sinx#

graph{sinx [-10, 10, -5, 5]}

Below is #y=sin(x-pi/3)#. Notice that it is exactly the graph #y=sinx# but moved to the right by #pi/3# units

graph{sin(x-pi/3) [-10, 10, -5, 5]}