Find cos theta/2

Question

If sin theta= 3/5

Answer 1

Hi, David.

 

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

 

Since sinθ = 3/5, cosθ = 4/5.

 

Therefore, (1+cosθ)/2  = 9/10, and cos(θ/2) = ±√.9.

 

Since 0 < θ < π,  we know that 0 < θ/2 < π/2, and cos(θ/2) is positive, cos(θ/2) = √.9 = 0.9487

 

I hope this helps.

Answer 2

sin theta = 3/5
theta = arc sin (3/5) = 36.87 deg
thus, cos (thteta/2) = cos (36.87/2) = cos (18.43) = 0.9487