Determine all of the solutions in the interval 0° = ? < 360°. sin(?/2) = sqrt 3 /2

Question

sin(θ/2) = √3/2

Answer 1

Greetings! Lets solve this shall we ?

So, we must find all solution(s) of the given equation sin(θ/2) = √(3)/2. We begin by solving for theta such that we take the sine inverse function of both sides such that

sin^-1(sin[θ/2]) = sin^-1(√(3)/2)

θ/2 = sin^-1(√(3)/2)...........Since sin^-1(√(3)/2) = 60^o, we obtain

θ/2 = 60^o........Finally, cross multiply such that

θ = 120^o

I hope this helped!