Given a point (x, y) on the unit circle, we can form a right triangle, as shown in the figure. Using the unit circle definitions allows us to extend the domain of trigonometric functions to all real numbers. The right triangle definition of trigonometric functions allows for angles between 0° and 90° (0 and in radians). A unit circle is a circle of radius 1 centered at the origin.

Trigonometric functions can also be defined as coordinate values on a unit circle. These functions are often written in their abbreviated forms. The following are the definitions of the trigonometric functions. Consider an angle θ as one angle in a right triangle. The output of a trigonometric function is a ratio of the lengths of two sides of a right triangle. The right-angled triangle definition of trigonometric functions is most often how they are introduced, followed by their definitions in terms of the unit circle. There are two main ways in which trigonometric functions are typically discussed: in terms of right triangles and in terms of the unit circle. Refer to the reference angles section below for more detail as well as a table of the signs of the six trigonometric functions in each quadrant. We can find the values of the other trigonometric functions in the same way. Similarly, since the value for cos(330°) in quadrant IV is positive, it has the same value as cos(30°). Since the values of cosine in quadrants II and III are negative, the value for cosine for the corresponding angles in quadrants II and III (150° and 210°) is. For example, the value of cosine for 30° or in the first quadrant is. Although the table does not include the multiples of each angle in each quadrant, we can use the table to find the values of the other angles the values are the same for each corresponding angle, taking the sign of the respective quadrant into consideration.

Sin cos tan sec csc cot