Determining sine, cosine, tangent, cotangent, secant, and cosecant through a right triangle

In order to find the trigonometric functions of arbitrary angle α, we assume a random right triangle ABC, which contains angle α.

Angle C is the right angle.

AC and BC sides are legs of the ABC triangle.

The AB is the hypotenuse of the ABC triangle.

Let us denote angle A as α.

The BC side opposite to angle α will be denoted as a.

The AC side adjacent to angle α will be denoted as b.

Hypotenuse AB will be denoted as c.

Determining trigonometric functions through a right triangle

# Definition of the sine

The sine of angle α is the ratio of the opposite leg to the hypotenuse:

Definition of the sine

# Definition of the cosine

The cosine of angle α is the ratio of the adjacent leg to the hypotenuse:

Definition of the cosine

# Definition of the tangent

The tangent of angle α is the ratio of the opposite leg to the adjacent leg:

Definition of the tangent

# Definition of the cotangent

The cotangent of angle α is the ratio of the adjacent leg to the opposite leg:

Definition of the cotangent

# Definitions of the secant and cosecant

The secant of angle α is the ratio of the hypotenuse to the adjacent leg:

The cosecant of angle α is the ratio of the hypotenuse to the opposite leg:

Definitions of the secant and cosecant