Question

How to graph cosine functions

Answer 1

You can graph this with some basic knowledge on how cos(α) behaves.

- The amplitude is 1, which means the graph is between -1 and +1.
- It starts at α=0, y=1, goes through y=0 at α=π/2, and is y=-1 at α=π
- It goes back to y=1 at α=2π
- The graph repeats every 2π

Using this you can draw a smooth curve. Make sure the curve is horizontal at y=+1 and y=-1. (I'm using α in stead of x, but you can choose).

To remember these values, imagine a circle of radius 1. You will walk it counterclockwise. Start at (1,0). A full round is 2π, so you can easily see where π/2, π and 3/4π are on the circle (0 is at 3 o clock, π/2 is at noon, and so forth).

Know that the cosine is actually the x coordinate of a point on the circle. Then you can see for yourself that cos(π/2)=0, since at "noon" on the circle, the x coordinate is 0. So you track what happens to the x coordinate as you travel around the circle. (I used α for the cos argument to avoid confusion with the x on the circle). For sine, it's the same thing, but then you would be tracking the y coordinate.

Hope this helps.