Wave Addition, Cosine Waves, and a₀
The idea, in my own words.
Wave addition is where you take a bunch of those lines we've been talking about in the last two parts, and combine them to take parts of each wave. It's like how a baby inherits half of their mom's genes and half of their dad's. Cosine is basically sine's evil twin. Instead of the equation being dividing the vertical and the diagonal sides of a right triangle, you take horizontal and diagonal. When you make the wave it looks like a sine wave but it's turned 90 degrees to the left. a₀ is how you make a wave oscillate without having a center of 0.
Worked example.
Take this example:
| θ | sin(θ) | f(θ) = 2 + 5·sin(θ) |
|---|---|---|
| 0° | 0 | 2 |
| 90° | 1 | 7 |
| 180° | 0 | 2 |
| 270° | -1 | -3 |
| 360° | 0 | 2 |
As we can see, a-zero works perfectly for these types of examples.
Carried question.