#### Introduction

- Given a right angled triangle:
- We have labelled:
- The angle as
**θ**. - The hypotenuse as
**h**, which is the longest side, and is opposite the right angle. - The adjacent side as
**a**, which is next to the angle. - The opposite side as
**o**, which is opposite the angle.

- sin, cos, and tan are functions which convert the angle to a ratio of two of the sides:

#### Example

- Given the triangle:
- We can calculate:

#### Code (Python)

```
import math
# python works in radians, not degrees
theta = math.radians(30)
print(math.sin(theta)) # prints 0.5
print(math.cos(theta)) # prints 0.866...
print(math.tan((theta))) # prints 0.577...
```

#### Notes

- sin, cos, and tan are sometimes called sine, cosine, and tangent.
- A simple way to remember the equations for sin, cos, and tan is
**sohcahtoa**:-
**soh**: **s**in **o**pposite **h**ypotenuse **cah**: **c**os **a**djacent **h**ypotenuse**toa**: **t**an **o**pposite **a**djacent

#### tan as a function of sin and cos

- If we re-arrange the equations for the opposite and adjacent:
- Then we can rewrite tan in terms of sin and cos:
- Which simplifies to:

#### Graphs of sin, cos, and tan

- We can plot sin on a graph, where:
- x is between 0 and 360
- y = sin(x)

- We see that sin(x) is always between -1 and 1

- And for cos:
- We see that cos(x) is just sin(x) shifted left by 90°

- And finally tan:
- We see that tan(90) and tan(270) aren't defined, as cos(90) and cos(270) are 0, which causes a divide by 0 error.