Question

The period of function $f\left(x\right)=\sin 3x\cos \left[3x\right]-\cos 3x\sin \left[3x\right],$ where [.] denotes the greatest integer function is

• A. $6$
• B. $3$
• C. $\frac{1}{3}$
• D. $\frac{1}{6}$

Answer 1

Answer: (C)

$\frac{1}{3}$

$f\left(x\right)=\sin 3x\cos \left[3x\right]-\cos 3x\sin \left[3x\right]f\left(x\right)=\sin (3x-\left[3x\right])f\left(x\right)=\sin \left(\left\{3x\right\}\right)x=\left[x\right]+\left\{x\right\}\left\{x\right\}=x-\left[x\right]$

Period of $f\left(x\right)=\frac{1}{3}$