Trigonometry
on the Circle

The applet beneath was created in GeoGebra, which is a small, free piece of dynamic geometry software that can be downloaded from: www.geogebra.org

An interactive demonstration of
the sine, cosine and tangent functions from the unit circle

The applet beneath was created in GeoGebra, which is a small, free piece of dynamic geometry software that can be downloaded from: www.geogebra.org

Use the slider to alter the angle and observe how the triangle generated gives the sine and cosine results for angles beyond just 90 degrees. Note that the tangent function is linked to the opposite and adjacent sides, although it is not especially obvious how - consider the triangle generated with the line labelled tan and note that it is similar to the one within the circle. Therefore the ratio of the corresponding sides must be equal.