Find the exact values of sin(θ/2), cos(θ/2), and tan(θ/2) for the given conditions.

Question

sec θ =
5
3
; 0° < θ < 90°

 

sin(θ/2) =


cos(θ/2) =

tan(θ/2)

Answer 1

If secθ = 5/3, then cosθ = 3/5.

 

So, sin(θ/2) = √[(1-cosθ)/2] = √[(1-3/5)/2] = √(1/5) = √5/5

 

      cos(θ/2) = √[(1+cosθ)/2] = √[(1+3/5)/2] = 2/√5 = 2√5/5

 

      tan(θ/2) = sin(θ/2) / cos(θ/2) = 1/2