Trigonometric Functions

Definition of Trigonometric Functions

In the coordinate plane, let the center be at the origin and a point on a circle with radius (where ).

Let the positive direction of the -axis be the initial side. When the angle represented by the terminal side is , the trigonometric functions for are defined as follows:

Here, , , and are called the sine function, cosine function, and tangent function, respectively. These are referred to as the trigonometric functions of .

1. The signs of trigonometric functions in each quadrant are as follows:

2. Quadrant	1st Quadrant	2nd Quadrant	3rd Quadrant	4th Quadrant

3. is not defined at (where is an integer).

Relationships Between Trigonometric Functions

If the angle represents the terminal side that intersects the unit circle at the point , the following hold true:

1. Since , , and (where ), we have:
   
2. Since point lies on the circle , the following equation holds: