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\ |
| Adjacent |
| |
|_______________________________________________________________________|

An easy method to remember

**dgm 1** is:

**SOH.CAH.TOA**
The sine, cosine and tangent of 30

^{0}, 45

^{0} and 60

^{0}, 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 45**^{0} = 1/√2

cos 45^{0} = 1/√2

tan 45^{0} = 1

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

The triangle in

**dgm 3** shows the following:

**
sin 60**^{0} = √3/2

cos 60^{0} = 1/2

tan 60^{0} = √3

sin 30^{0} = 1/2

cos 30^{0} = √3/2

tan 30^{0} = 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*