Question

Use periodicity of the trigonometric functions to find the exact value of $\tan 21\pi$

• A. $0$
• B. $1$
• C. $-1$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $0$

$\tan x$ has period $2\pi$

Which implies $\tan \left(x\right)=\tan (x+2\pi )$

$\tan \left(21\pi \right)=\tan (10\times 2\pi +\pi )=\tan \left(\pi \right)=0$ {consider 10 x 2$\pi$=$x$}

$\therefore \tan 21\pi =0$