find tan(θ) if sin(θ/2) = 16/34

find tan(θ) if sin(θ/2) = 16/34
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1 Answer

sinθ≡2sin(θ/2)cos(θ/2).

sin(θ/2)=16/34=8/17; cos(θ/2)240/289=√(1-64/289)=15/17.

sinθ=2(8/17)(15/17)=240/289.

Sine=opposite/hypotenuse, so adjacent2=hypotenuse2-opposite2=

2892-2402=(289-240)(289+240)=(49)(529).

adjacent=7×23=161.

tanθ=opposite/adjacent=240/161.

by Top Rated User (1.2m points)

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