What does tangent mean?

Tangent, a mathematical term, 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.

trigonometric function

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.

Tangent law

In a plane triangle, the tangent theorem shows that the quotient obtained by dividing the sum of any two sides by the difference between the first side and the second side is equal to the quotient obtained by dividing the tangent of half the sum of the diagonals of these two sides by the tangent of the difference between the diagonals of the first side and the second side.

Franciscus Vieta (Fran &; CcedilOisViète) once put forward the tangent theorem in his first book on trigonometry, Mathematical Rules Applied to Triangle. Modern middle school textbooks are rarely mentioned, for example, because China criticized the former Soviet Union and its pedagogy.

From 1966 to 1977, the tangent theorem in middle school mathematics textbooks has been deleted. But when there is no computer to help solve triangles, this theorem is easier to use logarithm to calculate projections and other problems than cosine theorem.

Tangent theorem: (a+b)/(a-b) = tan ((α+β)/2)/tan ((α-β)/2).