## Sohcahtoa

Table of Contents

## Definitions

Just an easy way to remember how Sine, Cosine and Tangent work:

**Soh**… (**S**ine = **O**pposite / **H**ypotenuse)

…**cah**… (**C**osine = **A**djacent / **H**ypotenuse)

…**toa**** (****T**angent = **O**pposite / **A**djacent)

## Right Triangle

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 longest one

## Sine, Cosine, & Tangent

Sine, Cosine, and Tangent are the 3 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 |

What are the sine, cosine and tangent of 60° ?

A 60° triangle has a hypotenuse (the longest side) of length 2, an opposite side of length √3 and an adjacent side of 1, like this:

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

Sine | soh… | sin(60^{o}) = √3/2 |

Cosine | …cah… | cos(60^{o}) = 1/2 |

Tangent | …toa | tan(60^{o}) = √3 |