Methods to Find Period of A Periodic Function

Methods to Find Period of A Periodic Function

• sinnx, cosnx, secnx, cosecnx, are periodic functions with period 2π and π according as n is odd or even.
• tannx, cotnx are periodic functions with period π (n even or odd).
• |sin x|, |cos x|, |tan x|, |cot x|, |sec x|, |cosec x| are periodic functions with period π.
• |sin x| + |cos x|, |tan x| + |cot x|, |sec x| + |cosec x| are periodic functions with period π/2.
• If f(x) is periodic function with period T then the function f(ax + b) is periodic with period T/|a|. For example sin 3x has period 2π/3, cos 5x has a period 2π/5 and tan(-7x+8) has a period π/7.
• If f₁(x) and f₂(x) be two trigonometric functions with periods T₁ and T2 then K₁ f₁(x) + K₂ f₂(x) = F(x) is a periodic function with its period as the LCM of T₁ and T₂.

For example if F(x) = 5 Sin x – 7 Sin 8x.

The period of Sin x and Sin 8x are 2π/1 and 2π/8

Hence the period of F(x) is the LCM of 2π/1 and 2π/8 = 2π.