If sin(θ)=−12/13, and θ is in Quadrant III, then what is cos(θ/2)?

Answer 1

Draw and label a diagram!

x = -5

cos θ = -5/13

cos (θ/2) = ±√[(1 + cos θ) / 2]

cos (θ/2) = ±√[(4/13) / 2]

cos (θ/2) = ±√4/13

cos (θ/2) is in QII. Cosine is negative in QII.

cos (θ/2) = -2√1/13