Question

Use periodicity of the trigonometric functions to find the exact value of $\sin {420}^o$

• A. $\frac{1}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $-1$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}$

$\sin x$ is periodic with period $2\pi$

$\therefore \sin x=\sin (x+2\pi )$

$\therefore \sin \left(420\right)=\sin (360+60)$

$=\sin \left(60\right)$

$=\frac{\sqrt{3}}{2}$