For the latitudinal direction, the real and imaginary components of the associated Legendre polynomials each possess ℓ−_"m"_ zeros, whereas for the longitudinal direction, the trigonometric sin and cos functions possess 2_"m"_ zeros.
For the latitudinal direction, the associated Legendre functions possess formula_50 zeros, whereas for the longitudinal direction, the trigonomentric formula_51 and formula_52 functions possess formula_53 zeros.