Trigonometric Functions

What is Trigonometric Functions?

Sine, cosine and tangent treated as functions of an angle rather than as ratios inside a right-angled triangle, so that every angle from 0 to 360 degrees has a value. The graph of y equals sin x starts at zero, rises to a maximum of 1 at 90 degrees, returns to zero at 180 degrees, falls to a minimum of minus 1 at 270 degrees and returns to zero at 360 degrees. The graph of y equals cos x is the same shape shifted, starting at 1, falling to zero at 90 degrees and to minus 1 at 180 degrees, then rising back through zero at 270 degrees to 1 at 360 degrees. The graph of y equals tan x rises without bound, has vertical asymptotes at 90 and 270 degrees where it is undefined, and repeats every 180 degrees. Because each curve takes most values twice in the interval, an equation such as sin x equals a given number normally has two solutions between 0 and 360 degrees, and an inverse key on a calculator returns only one of them; the second is recovered from the symmetry of the curve.

This definition is part of the Trigonometry chapter in Cambridge IGCSE Mathematics.