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.