**Right triangle:** A triangle in which one angle is a right angle

**Trigonometric functions on a circle with radius r:**

For any angle in standard position, let be the point on the terminal side of that is also on the circle .

,, , , , and .

**The trigonometric functions of an acute angle:** ** **

If is an acute angle of a right triangle, the six trigonometric functions of are as follow:

, , , , , and .

**Complementary angles:**

Two angles are called complementary if their sum equals to 90 degrees.

**Angle of elevation:**

The acute angle measured from the horizontal to a line-of-sight observation of the object.

**Angle of depression:**

The acute angle made by the line-of –sight observation of the object and the horizontal.

**The trigonometric functions of any angle:**

Let be an angle in standard position and let P(x,y) be a point, not the origin, on the terminal side that can be in any quadrant. If is the distance from the origin to the point P(x,y), then

, , , , , and

**Trigonometric identities:**

**, , , and . **