Find the exact values

Question

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

5 tan 𝜃 = 5;    −180° < 𝜃 < −90°

sin(𝜃/2)
cos(𝜃/2)
tan(𝜃/2)

Answer 1

tanθ = 1; - 45° < θ/2 < - 90°, θ/2 in quadrant IV;

cosθ = - 1/√[1 + tan²θ] = -1/√2.

sinθ/2 = - √(1 + 1/√2)/2 = - √(√2 + 1)/2

cosθ/2 = √(1 - 1/√2)/2 = √(√2 -1)/2

tanθ/2 = sinθ/2/cosθ/2 = - √(√2 +1)/(√2 - 1) = - (√2 + 1)

Answer 2

tan θ = 1

If θ is in Q III then θ = ?

sin θ = ?

cos θ = ?

Draw and label a diagram!