Question

use the half angle formula to find the exact value of sin15 degree

Answer 1

Question 27687

Half-angle formula for sine function is $\sin \left(\frac{x}{2}\right) = \sqrt{\frac{(1 - \cos x)}{2}}$ for $0 \leq x \leq \pi$ . One knows that table value of $\cos 30 = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$ . Hence,

$$\sin (15) = \sqrt {\frac {(1 - \frac {\sqrt {3}}{2})}{2}} = \sqrt {\frac {2 - \sqrt {3}}{4}} \approx 0.26.$$