matplotlib geostrophic wind plot
Your answer was incorrect because the axes were flipped and it didn't plot the entire line.

This was the correct answer I was looking for.

import matplotlib.pyplot as plt 
import numpy as np

# define the parameters
g = -9.81 # m/s^2
dZ = 60 # m
dx = 2e5 # m
omega = 7.2921e-5 # rad/s
phi = np.linspace(10,90) # deg
f = 2 * omega * np.sin(np.radians(phi)) # coriolis frequency, s^-1

# compute geostrophic wind, x-component
u_g = -1. * g/f * dZ/dx

# plot phi vs V_g
fig, ax = plt.subplots()
ax.plot(phi, u_g, color='#FF33CC')
ax.set_xlabel('$\phi$')
ax.set_ylabel('$V_{g}$ (m $s^-1$)')
plt.title('Geostrophic Wind vs. Latitude')
plt.show()