Question

Find the exact value of sin(-15)

Answer 1

`(√(6) - √(2) )/(4)` is the answer

Explanation:

I just took the test, and did the calculations.

Answer 2

`1)\ \ \ sin(- \alpha )=-sin \alpha \\2)\ \ \ cos2 \alpha =1-2sin^2 \alpha \ \ \ \Rightarrow\ \ \ 2sin^2 \alpha =1-cos2 \alpha \\\\ \Rightarrow\ \ \ sin \alpha = \sqrt{\frac{\big{1-cos2 \alpha}}{\big{2}}} \\\\\\sin(-15^0)=-sin15^0=-\sqrt{\frac{\big{1-cos30^0}}{\big{2}}} =-\sqrt{\frac{\big{1- ( √(3) )/(2) }}{\big{2}}} =-\sqrt{\frac{\big{2- √(3)}}{\big{4}}} =\\\\ =- (1)/(2) \sqrt{2- √(3)}`