The prime application of the trigonometric functions are triangle theorems. In a triangle, ,, and represent the lengths of the sides opposite to the angles, Δ the area , the circumradius, and the inradius. Then the following identities hold:
For a right‐angle triangle the following relations hold:
Because the trigonometric functions appear virtually everywhere in quantitative sciences, it is impossible to list their numerous applications in teaching, science, engineering, and art.