#
Section 12-6

#
Trigonometric Ratios

"Trigon" is greek for triangle, and "metric" is greek for measurement. The
trigonometric ratios
are special measurements of a
**
right triangle
**
(a triangle with one angle measuring 90
^{
o
}
). Remember that the two sides of a right triangle which form the right angle are called the
**
legs
**
, and the third side (opposite the right angle) is called the
hypotenuse
.

There are three basic trigonometric ratios:
**
sine
**
,
**
cosine
**
, and
**
tangent
**
. Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non-90
^{
o
}
angles.

Example:

Write expressions for the sine, cosine, and tangent of
*
A.
*

*
*

The length of the leg opposite
*
A
*
is
*
a
*
. The length of the leg adjacent to
*
A
*
is
*
b
*
, and the length of the hypotenuse is
*
c
*
.

The sine of the angle is given by the ratio "opposite over hypotenuse". So,

The cosine is given by the ratio "adjacent over hypotenuse".

The tangent is given by the ratio "opposite over adjacent".

Generations of students have used the mnemonic "SOHCAHTOA" to remember which ratio is which. (
**
S
**
ine:
**
O
**
pposite over
**
H
**
ypotenuse,
**
C
**
osine:
**
A
**
djacent over
**
H
**
ypotenuse,
**
T
**
angent:
**
O
**
pposite over
**
A
**
djacent.)