TRIGONOMETRY RATIOS

Trigonometric ratios

Main article: Trigonometric function

In this right triangle: sin A = a/c; cos A = b/c; tan A = a/b.

Trigonometric ratios are the ratios between edges of a right triangle. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure:

• Sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse.

${\displaystyle \sin A={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}={\frac {a}{c}}.}$

• Cosine function (cos), defined as the ratio of the adjacent leg (the side of the triangle joining the angle to the right angle) to the hypotenuse.

${\displaystyle \cos A={\frac {\textrm {adjacent}}{\textrm {hypotenuse}}}={\frac {b}{c}}.}$

• Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.

${\displaystyle \tan A={\frac {\textrm {opposite}}{\textrm {adjacent}}}={\frac {a}{b}}={\frac {a/c}{b/c}}={\frac {\sin A}{\cos A}}.}$

The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. See below under Mnemonics.