If sin(x) = 3/5 with x in the first quadrant, what is the exact value of sin(2x)?
Answer and explanation
Correct answer: C. 24/25
- Step 1: Since sin(x) = 3/5 in Quadrant I, cos(x) = sqrt(1 - (3/5)^2) = 4/5. Step 2. Double angle formula: sin(2x) = 2 sin(x) cos(x). Step 3. sin(2x) = 2 (3/5) (4/5) = 24/25. Answer: 24/25. Why not the others: 6/5 merely doubles 3/5 without cos(x).
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