Express sin(3*theta) in terms of sin(theta) using de Moivre's theorem.
Answer and explanation
Correct answer: A. sin(3theta) = 3sin(theta) - 4*sin^3(theta)
- Step 1: (cos(theta) + isin(theta))^3 = cos(3theta) + isin(3theta). Step 2. Imaginary part: 3cos^2(theta)sin(theta) - sin^3(theta) = 3(1 - sin^2(theta))sin(theta) - sin^3(theta) = 3sin(theta) - 4sin^3(theta). *Answer: sin(3theta) = 3sin(theta) - 4sin^3(theta). Why not the others:** This identity expresses triple angle purely in odd powers of sine.
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