Find sin theta/2

Question

If cos theta = -3/5

Answer 1

Hi, David.

 

The half angle formula:  sin(θ/2) =± √((1-cosθ)/2).

 

Therefore, (1-cosθ)/2 = (1+.6)/2 = .8.

 

sin(θ/2) = ±√(.8)   and  since π/2 < θ < 3π/2, Π/4 < θ/2 < 3π/4,  sin(θ/2) is ±√(.8).

 

I hope this helps.

 

Answer 2

cos theta = -3/5

theta = arc cos (-3/5) = 126.87 deg

thus, sin (thteta/2) = sin (126.87/2) = sin (63.43) = 0.8944