# Sohcahtoa

Sohca...*what?* Just an **easy way to remember** how Sine, Cosine and Tangent work:

Soh... |
Sine = Opposite / Hypotenuse |

...cah... |
Cosine = Adjacent / Hypotenuse |

...toa |
Tangent = Opposite / Adjacent |

## Right Triangle

OK, let's see what this is all about.

Firstly, the names **Opposite, Adjacent and Hypotenuse** come from the right triangle:

- "Opposite" is opposite to the angle θ
- "Adjacent" is adjacent (next to) to the angle θ
- "Hypotenuse" is the long one

**Adjacent** is always next to the angle

And **Opposite** is opposite the angle

## Sine, Cosine and Tangent

And **Sine**, **Cosine** and **Tangent** are the three main functions in trigonometry.

They are often shortened to **sin**, **cos** and **tan**.

The calculation is simply **one side of a right angled triangle divided by another side** ... we just have to know which sides, and that is where "sohcahtoa" helps.

For a triangle with an angle ** θ** , the functions are calculated this way:

Sine: |
soh... |
sin(θ) = opposite / hypotenuse |

Cosine: |
...cah... |
cos(θ) = adjacent / hypotenuse |

Tangent: |
...toa |
tan(θ) = opposite / adjacent |

### Example: what are the sine, cosine and tangent of 30° ?

A 30° triangle has a hypotenuse (the long side) of length **2**, an opposite side of length **1** and an adjacent side of
**√3**, like this:

Now we know the lengths, we can calculate the functions:

Sine |
soh... |
sin(30°) = \frac{1}{2} = 0.5 |

Cosine |
...cah... |
cos(30°) = \frac{1.732...}{2} = 0.866... |

Tangent |
...toa |
tan(30°) = \frac{1}{1.732...} = 0.577... |

(get your calculator out and check them!)

## How to Remember

I find "sohcahtoa" easy to remember ... but here are other ways if you like:

**S**ailors**O**ften**H**ave**C**urly**A**uburn**H**air**T**ill**O**ld**A**ge.**S**ome**O**ld**H**orses**C**an**A**lways**H**ear**T**heir**O**wners**A**pproach.**S**ome**O**ld**H**en**C**aught**A**nother**H**en**T**aking**O**ne**A**way.

## Practice Here: