The Sine Wave

The Sine Wave
This is a representation of various lingo language that is currently available. For those parents who are looking for Multiplication Worksheets you can check out the site where they have material for K-8 grades. For those going through AP math the examples below might be helpful.
As described in Sine & Cosine Definitions, t is the length of an arc on the unit circle. If the sine function is graphed with t on the horizontal axis and sin(t) on the vertical axis, this is the resulting curve:

Important points:

  • The curve oscillates between 1 and -1.
  • The curve repeats every 2pi.

A look at the unit circle shows the reasons. As proceeds around the unit circle, sin(t) goes up to 1 then down to -1, and then repeats as t keeps going around the circle. It repeats every 2pi because the circumference of the unit circle is2pi.

The graph of cosine is the same as sine, but shifted by -pi/2.


So sin(t) = cos(t – pi/2). For oscillation, either can be used to the same effect. A very interesting relation between sine and cosine is that the slope of the sine curve at any value of t is cos(t).