SOLUTION: Find cos 2θ. sin θ = 24/25 , θ lies in quadrant I.

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Question 920260: Find cos 2θ. sin θ = 24/25 , θ lies in quadrant I.
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
cos 2theta = 1-2sin^2theta
sin theta = 24/25
sin^2theta = 576/625

1-sin^2theta = 1-576/625
cos2theta=49/625

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find cos 2θ. sin θ = 24/25 , θ lies in quadrant I in which sin>0, cos>0
sin^2θ+cos^2θ=1
cos^2θ=1-sin^2θ
cosθ=√(1-sin^2θ)=√(1-(24/25)^2)=√(1-(576/625))=√(49/625)=7/25
cos2θ=cos^2θ-sin^2θ=49/625-576/625=-527/625
check:
sinθ=24/25
θ≈73.74˚
2θ≈147.48˚
cos2θ=cos(147.48˚)≈-0.8432...
Exact value=-527/625≈-0.8432...