Trig Functions and the Unit Circle

Recall our trig functions:

sin α = opp/hyp cos α = adj/hyp tan α = opp/adj

Below there are two figures. The first is the UNIT CIRCLE, a circle centered at the origin with radius one unit. The other figure is a triangle formed by the origin, a point on the circle and the perpendicular line to the x-axis from the point on the circle.

To change the triangle, move the slider, which changes the angle of the triangle. Notice the values of the point as you change the angle.

Find the sin α and cos α. Use the boxes to check your answer. What relationship is there between the point on the graph and the trig functions of α?

Jillian Maher, July 1, 2008, Created with GeoGebra