The tangent is one of the six fundamental trigonometric functions in mathematics. In a right triangle, it is the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle.
In the unit circle, the tangent of an angle alpha is the ratio of the sine to the cosine of that angle. $$ \tan \alpha = \frac {\sin \alpha} {\cos \alpha} $$ It is commonly denoted by the symbols tan or tg. The word "tangent" comes from the Latin "tangere," meaning "to touch."
The tangent function, written as tan (x), is one of the three primary trigonometric functions (alongside sine and cosine). It’s defined as the ratio of sine to cosine:
Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: Opposite is always opposite the angle. And Adjacent is always next to the angle.
The trigonometric functions most commonly used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less commonly used.
There are many methods that can be used to determine the value for tangent such as referencing a table of tangents, using a calculator, and approximating using the Taylor Series of tangent.
Tangent in geometry is defined as a line or plane that touches a curve or a curved surface at exactly one point. Learn about tangent definition along with properties and theorems.