# Sin, cos, tan

## In a nutshell

$\sin()$, $\cos()$, and $\tan()$ are the three main trigonometric functions and serve as the basis of trigonometry. Using the labels in a right-angled triangle, one can define these functions and their corresponding ratios.

### Labelling a triangle

#### Label | #### Meaning |

$x$ | The angle you're focusing on (you will either have to find out the value of $x$ or use it to find the length of a side) |

Hypotenuse | The longest side of the triangle |

Opposite | The side opposite the angle labelled $x$ |

Adjacent | The side next to the labelled angle *that isn't the hypotenuse* |

## The three trigonometric functions

These are the three main functions and their ratios:

#### Function name | #### Found on your calculator as | #### Corresponding ratio | #### Simplified version |

Sine | $\sin()$ | $\sin(x)=\frac{opposite}{hypotenuse}$ | SOH |

Cosine | $\cos()$ | $\cos(x)=\frac{adjacent}{hypotenuse}$ | CAH |

Tangent | $\tan()$ | $\tan(x)=\frac{opposite}{adjacent}$ | TOA |

**Note: **It is common and easy to just remember these three ratios as SOHCAHTOA.