The period of the function f(x) = log(cos 2x) | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To find the period of the function $f(x) = \log(\cos 2x) + \sin 4x$,we analyze the individual components.For the term $\log(\cos 2x)$,the function

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

(A) To find the period of the function $f(x) = \log(\cos 2x) + \sin 4x$,we analyze the individual components.For the term $\log(\cos 2x)$,the function is defined only when $\cos 2x > 0$.The period of $\cos 2x$ is $\frac{2\pi}{2} = \pi$.For the term $\sin 4x$,the period is $\frac{2\pi}{4} = \frac{\pi}{2}$.The period of the sum of two functions is the least common multiple $(LCM)$ of their individual periods.The $LCM$ of $\pi$ and $\frac{\pi}{2}$ is $\pi$.Thus,the period of the function $f(x)$ is $\pi$.

The period of the function $f(x) = \log(\cos 2x) + \sin 4x$ is :-

Similar Questions

The period of $\sin \theta \cos \theta$ is

The period of the function $|\sin(\pi x)|$ is

Which of the following functions has a period of $2\pi$?

Let $f(x) = \sin^2 x + \cos^4 x + 2$ and $g(x) = \cos(\cos x) + \cos(\sin x)$. Also,let the period of $f(x)$ and $g(x)$ be $T_1$ and $T_2$ respectively,then:

The period of $|\cos x|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module