Question

How do you find the exact values of sin(u/2), cos (u/2), tan (u/2) using the half angle formulas given `cos u= 3/5`, `0<u<pi/2`?

Answer 1

#cos x = 3/5

`2cos^2 (x/2) = 1 + cos x = 1 + 3/5 = 8/5 --> cos (x/2) = 0.89`

`2sin^2 (x/2) = 1 - cos x = 1 - 3/5 = 2/5 --> sin (x/2) = 0.48`

`tan (x/2) = sin (x/2)/cos (x/2) = 0.48/0.89 = 0.54`