Question 1121665
For simplicity, let theta = x
sin(x)cos(x) = 1/2
Using the identity cos(x) = sqrt(1 - sin^2(x)) we have:
sin(x)*sqrt(1 - sin^2(x)) = 1/2
Square both sides:
sin^2(x)(1 - sin^2(x)) = 1/4
sin^4(x) - sin^2(x) + 1/4 = 0
Factor:
(sin^2(x) - 1/2)(sin^2(x) - 1/2) = 0
This gives sin(x) = 1/sqrt(2)
In the interval 0 to 2pi, there are two solutions: x = pi/4 and 5*pi/4