Given that theta is acute and sin(theta) = 9/41, find sin(2 theta).
Answer and explanation
Correct answer: C. 720/1681
- Step 1: Since theta is acute, cos(theta) = sqrt(1 - sin^2(theta)) = 40/41.
- Step 2: sin(2 theta) = 2 sin(theta) cos(theta) = 2 x 9/41 x 40/41 = 720/1681.
Answer
720/1681.
Why not the others: '18/41' doubles sin(theta) instead of using the double-angle formula; '1519/1681' gives cos(2 theta); '40/41' gives cos(theta).
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