The Fundamentals of The Sine and Cosine

Take a quick look at their graph.

You immediately notice:

• The sine starts at 0

• The cosine starts at 1

• Both these graphs have a "pattern", or section that repeats every pi. You may conclude that the period for the functions sin(x) and cos(x) is 2pi. If you can't see it, take a look at the graph of sin(x) -- the yellow curve --, between the interval It's now easy to see you have a graph you can "copy and paste" infinitely to form the graph of sin(x).

  You can also observe the same for cos(x).

• Of an immediate conclusion is also the fact these graphs have a difference of pi/2 along the x-axis.

• This means that shifting the graph of sin(x) by 90 degrees or pi/2 gives the cosine, and vice-versa. You may get one of the graphs by shifting the other by pi/2 or 90 degrees along the x-axis.

We'll soon use these conclusions, right after we define the next two most important trigonometric functions:
The Tangent and Cotangent