(a) Evaluate $\int_0^{2\pi} \frac{1}{3 - 2\cos\theta + \sin\theta} d\theta$.
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Step 1: Rewrite the integral in terms of trigonometric functions Let's rewrite the denominator in terms of trigonometric functions: 3 - 2cosθ + sinθ = 3 - 2(1 - 2sin^2(θ/2)) + 2sin(θ/2)cos(θ/2) = 3 - 2 + 4sin^2(θ/2) + 2sin(θ/2)cos(θ/2) = 1 + 2sin(θ/2)(2sin(θ/2) + Show more…
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