This section defines the trigonometric ratios sine, cosine and tangent.

In a right triangle, there are two legs and a hypotenuse. In order to distinguish between two legs, we need a reference point. Mathematicians use one of the two acute angles as the reference point and call it the reference angle. With respect to the reference angle, one leg is the adjacent leg, or the leg right next to the reference angle; and the other leg is the opposite leg, or the leg on the opposite side of the triangle.

If two triangles are similar, the ratios of corresponding sides are equal.

Defining Trigonometric Ratios

Each of these three ratios has a special name.

Consider right triangle ABC

• ∠ A is a right angle
• BC is the hypotenuse of ΔABC
• With respect to ∠ B, AC is the opposite leg from ∠ B
• With respect to ∠ B, AB is the adjacent leg to ∠ B

Three Important Trigonometric Ratios

Trigonometric Ratio	Abbreviation	Ratio of Side Lengths	Example
Sine	sin	sin A =  Opposite Leg Hypotenuse	sin B =  AC BC
Cosine	cos	cos A =  Adjacent Leg Hypotenuse	cos B =  AB BC
Tangent	tan	tan A =  Opposite Leg Adjacent Leg	tan A =  AC AB