# Trigonometry/Functions

- See also
**Trigonometry/Polar**for an approach that is useful for -∞<θ<∞

## Fundamental trigonometry functionsEdit

There are six trigonometric functions in Trigonometry: sine, cosine, tangent, cotangent, secant, and cosecant.

## SineEdit

- Sine θ is the length of the leg opposite θ over the length of the hypotenuse:

## CosineEdit

- Cosine θ is the length of the leg adjacent to θ over the hypotenuse:

## TangentEdit

- Tangent of θ is the length of the leg on the opposite side of the triangle from the angle θ over the length of the leg of the triangle adjacent to the angle θ:

These three can be memorized by use of the name of the princess "Soh Cah Toa," meaning:

- "
**s**ine-**o**pposite-**h**ypotenuse **c**osine-**a**djacent-**h**ypotenuse**t**angent-**o**pposite-**a**djacent".

The remaining ratios are reciprocals of the previous ratios:

## CotangentEdit

- Cotangent θ is the reciprocal of tangent θ:

## SecantEdit

- Secant θ is the reciprocal of cosine θ:

## CosecantEdit

- Cosecant θ is the reciprocal of sine θ:

## Other considerationsEdit

- Since the hypotenuse of a right triangle is always the longest side, and
- If we divide both sides of each of these inequalities by the positive number , we get and

or and

## TableEdit

- See Table of functions.

## QuizEdit

## Other resourcesEdit

**Reading**: w:Trigonometric_Functions (Wikipedia)**Videos**:

- Basic Trigonometry (Youtube)
- Basic Trigonometry II (Youtube)