Given that theta is acute and sin(theta) = 16/65, find sin(2 theta).

Answer and explanation

Correct answer: B. 2016/4225

  1. Step 1: Since theta is acute, cos(theta) = sqrt(1 - sin^2(theta)) = 63/65.
  2. Step 2: sin(2 theta) = 2 sin(theta) cos(theta) = 2 x 16/65 x 63/65 = 2016/4225.
Answer
2016/4225.
Why not the others: '256/4225' squares sin(theta) instead of using the double-angle formula; '3713/4225' gives cos(2 theta); '63/65' gives cos(theta).

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