NDA 2019 Maths · Mathematics · Trigonometric Functions and Identities · easy

The fundamental period of the function f(x)=cos 3x/2 is

Single correct option

The fundamental period of the function

f(x)=\cos\dfrac{3x}{2}

Show answer and solution

Answer: (D) $\dfrac{4\pi}{3}$

The function

\cos kx

has period

\dfrac{2\pi}{|k|}

. With

k=\dfrac32

the period is

2\pi\times\dfrac23=\dfrac{4\pi}{3}

. Check:

x\to x+\dfrac{4\pi}3

changes the argument by

2\pi

. The option

3\pi

results from multiplying by

k

instead of dividing, and

\dfrac{2\pi}3

from inverting the factor.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake