What is the smallest positive period of the function y = cos 3x?

univerkov | March 11, 2021 | education

In order to find the smallest positive period of the function y = cos (3 * x), we use the fact that for the function y = cosx the smallest positive period is T = 2 * π. This means that at the smallest T = 2 * π, the equality cos (x + T) = cosx is fulfilled.
Suppose that for a given trigonometric function y = cos (3 * x), the angle T0 is the smallest positive period. Then, cos (3 * (x + T0)) = cos (3 * x). We have 3 * (x + T0) = 3 * x + 2 * π or 3 * x + 3 * T0 = 3 * x + 2 * π, whence 3 * T0 = 2 * π. We divide both sides of the last equality by 3. Then, we get: Т0 = 2 * π / 3.
Answer: The smallest positive period of the function y = cos (3 * x) is 2 * π / 3.

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