The period of the function f(x)= sin ( sin (x/5) ) is

Question

The period of the function f(x)= sin ( sin (x/5) ) is (A)  2π  (B)  (2π /5)  (C)  10π  (D)  5π

Tardigrade Admin · Accepted Answer

Given, f(x)= sin ( sin (x/5) ) ∴ f(x+10π )= sin [ sin ( (x+10π /5) ) ] = sin [ sin ( (x/5)+2π ) ] = sin ( sin (x/5) )=f(x) Hence, period of f(x) is 10π

Q. The period of the function $f (x) = sin (sin \frac{x}{5})$ is

$2 π$

$\frac{2 π}{5}$

$10 π$

$5 π$

Given, $f (x) = sin (sin \frac{x}{5})$ $∴$ $f (x + 10 π) = sin [sin (\frac{x + 10 π}{5})]$ $= sin [sin (\frac{x}{5} + 2 π)]$ $= sin (sin \frac{x}{5}) = f (x)$ Hence, period of $f (x)$ is $10 π$

Q. The period of the function f(x)=sin(sin5x​) is

2π

52π​

10π

5π