The period of the function f(x) = cos 4x + ta | vedclass

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

Question

(A) The period of $\cos(ax)$ is $\frac{2\pi}{|a|}$. Thus, the period of $\cos 4x$ is $T_1 = \frac{2\pi}{4} = \frac{\pi}{2}$.The period of $	an(bx)$ i

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

(A) The period of $\cos(ax)$ is $\frac{2\pi}{|a|}$. Thus, the period of $\cos 4x$ is $T_1 = \frac{2\pi}{4} = \frac{\pi}{2}$.The period of $	an(bx)$ is $\frac{\pi}{|b|}$. Thus, the period of $	an 3x$ is $T_2 = \frac{\pi}{3}$.The period of the sum of two periodic functions is the least common multiple $(LCM)$ of their individual periods.We need to find $	ext{LCM}\left(\frac{\pi}{2}, \frac{\pi}{3}ight)$.To find the $LCM$ of fractions $\frac{a}{b}$ and $\frac{c}{d}$, we use the formula $\frac{	ext{LCM}(a, c)}{	ext{HCF}(b, d)}$.Here, $	ext{LCM}(\pi, \pi) = \pi$ and $	ext{HCF}(2, 3) = 1$.Therefore, the period is $\frac{\pi}{1} = \pi$.

The period of the function $f(x) = \cos 4x + \tan 3x$ is

Similar Questions

The value of $n \in \mathbb{Z}$ for which the function $f(x) = \frac{\sin(nx)}{\sin(x/n)}$ has $4\pi$ as its period,is

The function $f(x) = |\sin 4x| + |\cos 2x|$ is a periodic function with period

The period of $\sin^2 x$ is

The period of the function $f(\theta) = \sin \frac{\theta}{3} + \cos \frac{\theta}{2}$ is (in $\pi$)

The period of the function $f(x) = e^{\log(\sin x)} + (\tan x)^3 - \operatorname{cosec}(3x - 5)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module