## Essential University Physics: Volume 1 (3rd Edition)

The proof is below; $h_1=a$, and $h_2=b$.
If the two components are out of phase by $\pi/2$, one is a cosine function, and the other will be a sine function. We will call the amplitudes $h_1$ and $h_2$. Thus: $\frac{x^2}{h_1^2}=cos^2 \omega t$ $\frac{y^2}{h_2^2}=sin^2 \omega t$ Thus, we see that it is an ellipse, and we see that $h_1=a$, and $h_2=b$.