The period of f(x)= sin (2π x/3)+ cos (π x/2) is

Question

The period of f(x)= sin (2π x/3)+ cos (π x/2) is (A) 3 (B) 4 (C) 6 (D) 12

Tardigrade Admin · Accepted Answer

Since, sin (2π x/3) and cos (π x/2) are periodic functions with periods (2π /2π /3)=3 and (2π /π /2)=4, respectively. Therefore, f(x) is periodic with period and equal to LCM of 3 and 4, i.e. 12.

Q. The period of $f (x) = sin \frac{2 π x}{3} + cos \frac{π x}{2}$ is

3

4

6

12

Since, $sin \frac{2 π x}{3}$ and $cos \frac{π x}{2}$ are periodic functions with periods $\frac{2 π}{2 π /3} = 3$ and $\frac{2 π}{π /2} = 4,$ respectively. Therefore, $f (x)$ is periodic with period and equal to LCM of 3 and 4, i.e. 12.

Q. The period of f(x)=sin32πx​+cos2πx​ is

3

4

6

12

Since, sin32πx​ and cos2πx​ are periodic functions with periods 2π/32π​=3 and π/22π​=4, respectively. Therefore, f(x) is periodic with period and equal to LCM of 3 and 4, i.e. 12.

Q. The period of $f (x) = sin \frac{2 π x}{3} + cos \frac{π x}{2}$ is

Since, $sin \frac{2 π x}{3}$ and $cos \frac{π x}{2}$ are periodic functions with periods $\frac{2 π}{2 π /3} = 3$ and $\frac{2 π}{π /2} = 4,$ respectively. Therefore, $f (x)$ is periodic with period and equal to LCM of 3 and 4, i.e. 12.