Adding two waves

You will add two waves point by point, and check the result against the formula for the amplitude of the sum.

The idea. A wave is $y = a\sin(kx - \omega t + \phi)$. Two waves of the same $k$ and $\omega$ add to a wave of amplitude $A = \sqrt{a_1^2 + a_2^2 + 2a_1a_2\cos\phi}$. For equal amplitudes, $A = 2a\cos(\phi/2)$.

Your tasks.

1. In wave, return the displacement $a\sin(kx - \omega t + \phi)$.
2. In equal_amplitude, return $2a\cos(\phi/2)$, as a size (use abs).
3. In general_amplitude, return the amplitude for two different amplitudes.
4. In largest_sum, return the largest value of the sum of the two waves at $x = 0$, over one period, using wave.