In Rt△ABC (right triangle), ∠C = 90, AB is the opposite side C of ∠ C, BC is the opposite side A of ∠A, AC is the opposite side B of ∠B, and the tangent function is tanB=b/a, that is, tanB=AC/BC.

That is, in a right triangle, if the acute angle is a, then tan ∠ a = the value of the opposite side compared with the adjacent side.

For example, a right triangle ABC with a side length of 3: 4: 5, AB = 3, BC = 4, AC = 5,

Then tan ∠ a = 4: 3.

Extended data:

Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.

Because of the periodicity of trigonometric function, it does not have the inverse function in the sense of single-valued function.

Trigonometric functions have important applications in complex numbers. Trigonometric function is also a common tool in physics.

In Rt△ABC, if the acute angle A is determined, then the ratio of the opposite side to the adjacent side of the angle A is determined. This ratio is called the tangent of angle α, and is written as tanA.

That is, the opposite side of tanA = the adjacent side of ∠ a/∠ a.