Question

What is the exact value of sin(5π/12)?

(please give steps)​

Answer 1

0.966053748

Explanation:

`\sin \bigg( (5\pi)/(12) \bigg) \\ = \sin \bigg( (5 * 180 \degree)/(12) \bigg) \\ = \sin ( 5 * 15 \degree) \\ = \sin ( 75 \degree) \\ = \sin ( 45 \degree + 30 \degree) \\ = \sin 45 \degree * \cos 30 \degree + \cos 45 \degree * \sin 30 \degree \\ \\ = (1)/( √(2) ) * ( √(3) )/(2) + (1)/( √(2) ) * (1)/(2) \\ \\ = ( √(3) )/(2 √(2) ) + (1)/(2 √(2) ) \\ \\ = ( √(3) + 1)/(2 √(2) ) \\ \\ = (1.732 + 1)/(2 * 1.414) \\ \\ = (2.732)/(2.828) \\ \\ = 0.966053748`