alleryIf sin θ = 12/13 (acute), find tan(θ/2):
A5/12
BCannot determine
C1/5
D2/3
Answer & Solution
Correct answer: C. 1/5
For acute θ with sinθ = 12/13: cosθ = 5/13 (positive in Q1).
tan(θ/2) = sinθ/(1 + cosθ) = (12/13)/(1 + 5/13) = (12/13)/(18/13) = 12/18 = 2/3. Hmm answer A is 1/5
my calc gives 2/3. Let me recheck.
tan(θ/2) = (1 - cosθ)/sinθ = (1 - 5/13)/(12/13) = (8/13)/(12/13) = 8/12 = 2/3. So actually 2/3 is correct, which matches option C, not A. Setting answer to C.
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