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If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):

A1/3
B3/4
C2/3
D1/5
Answer & Solution
Correct answer: C. 2/3
cos θ = √(1 − sin²θ) = √(1 − 144/169) = √(25/169) = 5/13 (positive in Q1). We have tan(θ/2) = (1 − cos θ)/sin θ. That is tan(θ/2) = (1 − 5/13)/(12/13). That is tan(θ/2) = (8/13)/(12/13). That is tan(θ/2) = 8/12. So tan(θ/2) = 2/3.
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