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 $\frac{\sin x}{\cos 3x} + \frac{\sin 3x}{\cos 9x} + \frac{\sin 9x}{\cos 27x} + \frac{\sin 27x}{\cos 81x}$ is

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

If the period of the function $f(x) = \sin 5x \cos 3x$ is $\alpha$,then $\cos \alpha =$

The period of $\sin ^4 x + \cos ^4 x$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module