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The range of the polar angle \( \theta \) in spherical coordinates is

  • A.\( -\pi \) to \( \pi \)
  • B.\( 0 \) to \( \pi/2 \)
  • C.\( 0 \) to \( \pi \)
  • D.\( 0 \) to \( 2\pi \)

Answer: C

Measured from the positive z axis, the polar angle reaches \( \pi \) at the negative z axis and that is the whole of its range; the azimuthal angle then sweeps the full \( 2\pi \) round. Allowing \( \theta \) to exceed \( \pi \) would cover space twice.

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