Question

Solve each equation on the interval 0 less than or equal to theta less than 2pi

2sintheta+1=0

Answer 1

2sintheta = -1
sintheta= -1/2
as sin is negative , therefore the value of theta lies in third quadrant and fourth quadrant

Answer 2

sintheta = sin (pi + pi/3) or sintheta = sin(2pi- pi/3)
theta = 4pi/3 or theta = 5pi/3