If a is in the third quadrant and sin a = -1/4, find the exact value of sin (a + π /3).

Question

If a is in the third quadrant and sin a = -1/4, find the exact value of sin (a + π /3).

Answer 1

sin(a + π/3) = sinacosπ/3 + cosasinπ/3 = -1/4·1/2 - √(1 - 1/16)·√3/2 = - 1/8 - 3√5/8 = - (1 + 3√5)/8