Question

Find the value of the trigonometric function $\sin (-\frac{11\pi }{3})$.

Answer 1

$\sin (-\frac{11\pi }{3})$ = −$\sin (-\frac{11\pi }{3})$ {∵sin(−𝑥)=−sin⁡𝑥 }
= −$\sin \left(\frac{12\pi -\pi }{3}\right)$
= −$\sin (4\pi -\frac{\pi }{3})$
Values of sin⁡𝑥 repeat after an interval of 2𝜋,
hence ignoring 4𝜋 i.e., 2(2𝜋)
∴ $\sin (-\frac{11\pi }{3})$= −$\sin (-\frac{\pi }{3})$ = −$(-\sin \left(\frac{\pi }{3}\right))$
⇒$\sin (-\frac{11\pi }{3})$=$\sin \left(\frac{\pi }{3}\right)$ = $\frac{\sqrt{3}}{2}$