The period of the function sin left( frac{pi | vedclass

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

Question

(A) The period of a function $f(x) = \sin(ax)$ is given by $T = \frac{2\pi}{|a|}$.For the term $\sin \left( \frac{\pi x}{2} \right)$,the period $T_1 =

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) The period of a function $f(x) = \sin(ax)$ is given by $T = \frac{2\pi}{|a|}$.For the term $\sin \left( \frac{\pi x}{2} ight)$,the period $T_1 = \frac{2\pi}{\pi/2} = 4$.For the term $\cos \left( \frac{\pi x}{2} ight)$,the period $T_2 = \frac{2\pi}{\pi/2} = 4$.The period of the sum of two periodic functions is the least common multiple ($L$.$C$.$M$.) of their individual periods.Therefore,the period of $\sin \left( \frac{\pi x}{2} ight) + \cos \left( \frac{\pi x}{2} ight) = 	ext{L.C.M. of } (4, 4) = 4$.

The period of the function $\sin \left( \frac{\pi x}{2} \right) + \cos \left( \frac{\pi x}{2} \right)$ is

Similar Questions

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

The period of $\cot 3x - \cos (4x + 3)$ is

The period of $\cos (3x + 5) + 7$ is

The period of the function $f(x) = \frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right) - 5 \sec \left(\frac{5 \pi x}{3}\right)}$ is

If the period of the function $f(x) = \frac{\tan 5x \cos 3x}{\sin 6x}$ is $\alpha$,then find the value of $f\left(\frac{\alpha}{8}\right)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module