Trigonometry Problem

Question

Find the exact value of sin(θ/2),given that tanθ = (8/15) and π<θ<(3π/2)

 

π=Pi

 

θ=Theta

Answer 1

tan(θ) = opp/adj =8/15 so the hyp =17 so cos(θ)=15/17

 

using the identity sin²(θ/2)=1/2(1-cos(θ))=1/2(1-15/17)=1/17 so

 

sin(θ/2)=+-√1/17 and since θ in in the third quadrant  choose the (-) sign

 

Jim