Find all solutions of the equation in the interval [0,2pi). 2sin theta+1=0.

Question

Write answer in radians in terms of pi.

Answer 1

2sinθ+1 = 0
2sinθ = -1
sinθ = -1/2
sin π/6 = 1/2, so using that as a reference angle in QIII and QIV, we get the solutions

π + π/6 and 2π - π/6