Note that when cosσ_i = 0 = cosσ' while δiq and δq' are positive σ_i = 90º (½π) = σ' and cscσ_i = 1 = cscσ' while when δiq and δq' are negative σ_i = 270º (3π/2) = σ' and cscσ_i = -1 = cscσ'. Furthermore, when cosσ_i = ±1 = cosσ', while δiq and δq' are positive σ_i = 0º (0) = σ' and when negative σ_i = 180º (π) = σ', in both cases cscσ_i = ± ∞ = cscσ'.