## Trigonometric functions on a coordinate system

Given a coordinate system, an angle (a radian  on the unit circle) always starts from the positive -axis, that is, from the point . We have the radian  if the angle with the terminal side  is constructed counterclockwise.

We have if it is clockwise.

In this setting of coordinate system, the cosine and the sine functions of  are defined by

That is, the point  on the unit circle with the radian  is given by

The other trigonometric functions of  are then determined by (1-2) and (1-3).

Department of Mathematics