SOLUTION: If angle θ is an acute angle such that cosθ = 1/4, find tan (theta/2).

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Question 890240: If angle θ is an acute angle such that cosθ = 1/4, find tan (theta/2).
Answer by lwsshak3(11628) About Me  (Show Source):
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If angle θ is an acute angle such that cosθ = 1/4, find tan (theta/2).
sinθ=√1-cos^2θ=√(1-1/16)=√(15/16)=√15/4
Identity: tan(θ/2)=sinθ/(1+cosθ)=√15/4/(1+1/4)=√15/4/(5/4)=√15/5
..
Check:
cosθ=1/4
θ≈75.52˚
θ/2≈37.76˚
tan(θ/2)=tan(37.76)≈0.7746…
Exact value=√15/5≈0.7746…