Theory

The trigonometric values for angles between $0$ and $90$ degrees can be defined as dimensions on the unit circle as shown below. Sine and cosine are lengths of half chords, tangent is a measurement on the tangent line. Compare these values to those given on your calculator. (Click ‘show values’ twice).

With this diagram (without clicking on ‘show values’), you can order the trig ratios according to size (although for some angles this is more obvious than others). You can also make trig pairs – for example, $\sin(20^{\circ})=\cos(70^{\circ})$ . You can understand that sine and cosine have both a minimum value and a maximum value, however tangent does not have a maximum value. The tangent of 90 degrees is undefined.