This clip gives the definitions of the trigonometric functions sine, cosine and tangent.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

A right triangle has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle.

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Students often use mnemonics to remember facts and relationships in trigonometry. For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, as in SOH-CAH-TOA.

Sine = Opposite ÷ Hypotenuse
Cosine = Adjacent ÷ Hypotenuse
Tangent = Opposite ÷ Adjacent

Alternatively, one can devise sentences which consist of words beginning with the letters to be remembered. For example, to recall that Tan = Opposite/Adjacent, the letters T-O-A must be remembered. Any memorable phrase constructed of words beginning with the letters T-O-A will serve.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments.

In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane.

In mathematics, the trigonometric functions are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle.

Trigonometry is a branch of mathematics that deals with triangles, particularly those plane triangles in which one angle has 90 degrees (right triangles). Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships.