If tan(theta) = 4/3 and theta lies in the first quadrant, find sin(2*theta).
Answer and explanation
Correct answer: C. 24/25
- Step 1: Construct a reference triangle: opposite = 4, adjacent = 3, hypotenuse = sqrt(4^2 + 3^2) = 5.
- Step 2: Find sin(theta) = 4/5 and cos(theta) = 3/5.
- Step 3: Apply double-angle formula: sin(2theta) = 2 sin(theta) cos(theta) = 2 (4/5) * (3/5) = 24/25.
Answer
24/25.
Why not the others: Option 7/25 evaluates cos(2*theta) = cos^2 - sin^2 = 9/25 - 16/25 = -7/25. Option 12/25 forgets the factor of 2. Option 16/25 squares sin(theta).
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