Question

How do you find the period of $y = \cos \left( {2x} \right)$ ?

Answer 1

Hint : All the trigonometric functions are periodic in nature. This means that they repeat their values after a regular interval of time .The fundamental period of sine and cosine functions is $2\pi$ radians and that of tangent function is $\pi$ radians. Now, we have to find the fundamental period of the function $y = \cos \left( {2x} \right)$ as given in the question.

Complete step by step solution:
In the problem given to us, we have to find the fundamental period of the function
$y = \cos \left( {2x} \right)$ .
We know that the fundamental period of the cosine function
$y = \cos \left( x \right)$ is $2\pi$ radians.
Period of trigonometric functions can be easily computed using a technique.
The period of the trigonometric function $y = \cos \left( {kx + c} \right)$ can be calculated easily by dividing the fundamental period of the original trigonometric function by the constant, k.
So, in the case of $y = \cos \left( {2x} \right)$ , the period is $\left( {\dfrac{{2\pi }}{2}} \right) = \pi$ radians.
Hence, the period of $y = \cos \left( {2x} \right)$ is $\pi$ radians
So, the correct answer is “ $\pi$ radians”.

Note : Periodic functions are the functions that repeat its value after a regular interval of time. Any function that does not repeat its value after a certain time interval is known as aperiodic function. Now, there can be multiple periods of a function. But only the smallest time interval after which the function repeats its value is called the fundamental period of the function.