Physics · Mathematical Methods
If θ and φ are respectively the polar and azimuthal angles on a unit sphere, what are the average values ⟨cos2(θ)⟩ and ⟨sin2(θ)⟩?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1⟨cos2(θ)⟩ = 1/3 and ⟨sin2(θ)⟩ = 2/3✓
- 2⟨cos2(θ)⟩ = 3/4 and ⟨sin2(θ)⟩ = 1/4
- 3⟨cos2(θ)⟩ = 1/2 and ⟨sin2(θ)⟩ = 1/2
- 4⟨cos2(θ)⟩ = 2/3 and ⟨sin2(θ)⟩ = 1/3
Correct answer
⟨cos2(θ)⟩ = 1/3 and ⟨sin2(θ)⟩ = 2/3
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