In mathematics the sine, cosine and tangent of an acute angle in a right-angled triangle are defined in terms of the sides of the triangle as follows:

```________________________________________________________________________
|                                                                       |
| dgm 1    |\                      sin = opposite/hypotenuse  : S = O/H |
|          | \                                                          |
|          |  \                    cos = adjacent/hypotenuse  : C = A/H |
|          |   \                                                        |
|          |    \                  tan = opposite/adjacent    : T = O/A |
|  Opposite|     \ Hypotenuse                                           |
|          |      \                                                     |
|          |       \                                                    |
|          |        \                                                   |
|          |        /\                                                  |
|          |_______|_x\                                                 |
|                                                                       |
|_______________________________________________________________________|
```

An easy method to remember dgm 1 is: SOH.CAH.TOA

The sine, cosine and tangent of 300, 450 and 600, can be expressed exactly in surd form and are worth remembering.

```________________________________
|                               |
| dgm 2    |\                   |
|          | \                  |
|          |  \                 |
|          |   \                |
|          |    \    __         |
|        1 |     \  \|2         |
|          |      \             |
|          |       \            |
|          |        \           |
|          |        /\          |
|          |_______|45\         |
|                               |
|                1              |
|_______________________________|
```

The triangle in dgm 2 shows the following:

sin 450 = 1/√2

cos 450 = 1/√2

tan 450 = 1

```________________________________
|                               |
| dgm 3       /|\               |
|            / | \              |
|           /  |30\             |
|          /   |---\            |
|         /    |    \           |
|        /     |     \  2       |
|       /  __  |      \         |
|      /  \|3  |       \        |
|     /        |        \       |
|    /\        |        /\      |
|   /60|_______|_______|60\     |
|                    1          |
|_______________________________|
```

The triangle in dgm 3 shows the following:

sin 600 = √3/2

cos 600 = 1/2

tan 600 = √3

sin 300 = 1/2

cos 300 = √3/2

tan 300 = 1/√3

Note - The standard way to measure angles in mathematics is anticlockwise from the positive-X direction. But I did it the other way for ease of ascii art...
Thank you hobyrne for pointing that out