Evaluate the exact value of cos(2*theta) given that sin(theta) = 0.6.
Answer and explanation
Correct answer: B. 0.28
- Step 1: Recall the double-angle identity: cos(2theta) = 1 - 2sin^2(theta).
- Step 2: Calculate sin^2(theta) = 0.6^2 = 0.36.
- Step 3: Substitute: cos(2theta) = 1 - 2(0.36) = 1 - 0.72 = 0.28.
Answer
0.28.
Why not the others: Option 0.64 computes cos^2(theta) = 1 - 0.36 = 0.64. Option -0.28 reverses the subtraction order (0.72 - 1). Option 0.48 calculates 2sin(theta)cos(theta) incorrectly.
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