Given that theta is acute and sin(theta) = 15/17, find sin(2 theta).
Answer and explanation
Correct answer: A. 240/289
- Step 1: Since theta is acute, cos(theta) = sqrt(1 - sin^2(theta)) = 8/17.
- Step 2: sin(2 theta) = 2 sin(theta) cos(theta) = 2 x 15/17 x 8/17 = 240/289.
Answer
240/289.
Why not the others: '225/289' squares sin(theta) instead of using the double-angle formula; '8/17' gives cos(theta); '15/17' gives sin(theta) itself.
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