Adding sine waves

1. How do you add two sine equations?
2. How do you add sine and cosine waves?

How do you add two sine equations?

cosφ = sinφ tanφ= ( E20 sin δ Eθ0 )(E10 + E20 cosδ E20 sin δ ) = E10 + E20 cosδ Eθ0 , which completes the derivation. As a check, consider the case of equal amplitudes, E10 = E20 ≡ E0. Then, using the above results, Eθ0 = √2E0(1 + cosδ) . (1 + cosδ), we end up with: Eθ0 = 2E0| cos(δ/2)| .

How do you add sine and cosine waves?

We can add together a sine and a cosine curve. Their sum can be obtained graphically by adding the y-values of the two curves. It turns out that, if the waves have the same period, this will produce another trigonometric graph with a change in amplitude and a phase shift.