Given that theta is acute and sin(theta) = 12/13, find sin(2 theta).
Answer and explanation
Correct answer: A. 120/169
- Step 1: Since theta is acute, cos(theta) = sqrt(1 - sin^2(theta)) = 5/13.
- Step 2: sin(2 theta) = 2 sin(theta) cos(theta) = 2 x 12/13 x 5/13 = 120/169.
Answer
120/169.
Why not the others: '144/169' squares sin(theta) instead of using the double-angle formula; '5/13' gives cos(theta); '12/13' gives sin(theta) itself.
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