Possible angles for internal gravity wave propagation

[contempquant]

Homework Statement

Internal gravity waves are generated along the coast of Norway by the principal lunar semidiurnal surface tide (known as the M2 tide) of period 12.42 h. If the stratification frequency N is 2 x 10^-3rad s^-1, at which possible angles can the energy propagate with respect to the horizontal?

Homework Equations

$$\omega={\pm}Ncos{\theta}$$

The Attempt at a Solution

Period, T is 12.42 hours = 44712 seconds

angular frequency is $$\omega=\frac{2{\pi}}{T}=1.41{\times}10^{-4}$$

$$N=2{\times}10^{-3}$$

Rearranging $$\omega={\pm}Ncos{\theta}$$ in terms of theta gives $$\theta=cos^{-1}{\frac{\omega}{\pm{N}}}$$

Giving theta values of 85.96 and 94.04, but this can't be right as i thought the maximum value of theta could be 90 degrees above the horizontal? can anyone see where I'm going wrong?

 

[contempquant]

no one knows?