The circle below is drawn in a coordinate system where the
circle's center is at the origin and has a radius of 1. This circle
is known as a unit circle.
The x and y coordinates for each point along
the circle may be ascertained by reading off the values on the
x and y axes. If you picture a right triangle
with one side along the x-axis:
then the cosine of the angle would be the x-coordinate
and the sine of the angle would be the y-coordinate. Since
both the coordinates are defined by using a unit circle, they are
often called circular functions.
Example:
Solve the equation sin v = 0.5 with the unit
circle.
If we examine the figure below, it is evident that there are two
solutions to the problem:
We arrive at the first solution by using a pocket calculator and
keying:
Since half a revolution is 180 degrees, we ascertain the other
angle by:
Videolesson: solve the given equation using the
unit circle Sin Ѳ = -1