Function defined from an arc of a circle or from the value of the angle at the centre corresponding to an arc of a circle.

A function *f* is a circular function on a unit circle C if and only if f: \(\mathbb{R}\) → C : | *t *|→ (*a, b*) where | *t* | is the measure of an arc on C and (*a, b*) is the ordered pair of coordinates of the end point P of the arc of measure | *t* |.

- The “circular function” is often called a “
*winding function*.” - The numbers
*a*and*b*are called the cosine and sine of the angle*θ*formed by the x-axis and the radius OP. - The functions that align the values
*a*and*b*to an angle*θ*of a unit circle are also circular functions.

A circular function P is a function in which every number *t* of the number line \(\mathbb{R} \) is made to correspond to a point P (*t*) on a unit circle centred on the origin of the Cartesian plane. On the unit circle C, to each arc measure, there corresponds a point of the circle:

- à | t | = 0 corresponds the ordered pair (1, 0)
- à | t | = π/2 corresponds the ordered pair (0, 1)
- à | t | = π corresponds the ordered pair (–1, 0)
- à | t | = 3π/2 corresponds the ordered pair (0, –1)
- à | t | = 2π corresponds the ordered pair (1, 0)