The trigonometric functions with which we are most familiar are sine and cosine. From them, we can obtain tangent, and also the reciprocals secant, cosecant and cotangent. In the past, mathematicians have used many other trigonometric functions too. Some of these are illustrated below.

A unit circle, a radius and a tangent with points of intersection labelled.

Find the following lengths, in terms of \(\sin\theta\) and \(\cos \theta\).

We have one angle \(\theta\) given on the diagram, so which lengths can we find using that?

Are there any other angles that are also \(\theta\)?

How many right-angled triangles are there in the diagram?