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 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