4 tan(1/2)(x+pi/4)

Question

Find the period in radians.

Answer 1

Consider the period of tanθ. Tangent is 0 when sine is zero. This occurs when θ=nπ, where n is an integer, so θ=0, π, 2π, 3π, ... The period of tanθ is therefore π radians.

Now consider ½(x+π/4)=x/2+π/8.

To find the period p of tan(½(x+π/4)), we need to find when ½(x+p+π/4)-½(x+π/4)=π.

Therefore p/2=π, p=2π, so the period is 2π radians (about 6.28).