SOLUTION: determine the period of y = tan 2x

Question 552469: determine the period of y = tan 2x
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
first you have to find the period for y = tan(x)
that is not 360 degrees as you might suppose.
tan x repeats every 180 degrees.
it's normal period is therefore 180 degrees.
the period is determined by the normal period divided by the frequency.
that would make tan(2x) period equal to 180/2 = 90 degrees.
below is a graph of tan(x)

those vertical lines are at 90 degrees (pi/2) and 270 degrees (3pi/2)
that's a period of 180 degrees (pi).
below is a graph of tan(2x)

those vertical lines are now at 45 degrees (pi/4) and 135 degrees (3pi/4)
that's a period of 90 degrees (2pi/4 or pi/2)
the frequency was doubled (2x instead of x).
the period was halved (90 degrees instead of 180 degrees).

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