y=5tan1/2(x+pi/4)
What is the period?
argument of tan = (x/2 + pi/8)
when x = 0 right now argument of tan = (pi/8)
what will x be when this is bigger by two pi?
(x/2 + pi/8) = (2 pi + pi/8)
or x/2 = 2 pi
x = 4 pi = period
or
how much x has to increase to go a whole way around 2 pi radians
Oh, sorry, tangent repeats every pi, not 2 pi
so period is 2 pi, not 4 pi
To find the period of the function y=5tan(1/2(x+π/4)), we can use the fact that the period of the tangent function is π. The general formula for the period of the tangent function is T = π / |B|, where B is the coefficient of x in the argument of the tangent function.
In this case, the coefficient of x is 1/2. So, the period of the function y=5tan(1/2(x+π/4)) is given by T = π / |1/2| = 2π.
Therefore, the period of the function y=5tan(1/2(x+π/4)) is 2π.