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tangent

tangent

1 7.2
A ratio of the side opposite an angle to the side next to it in a right triangle
  • noun
  • /ˈtæn.dʒənt/
  • Specialized
translation icon : tangente
  • In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
  • hyperbolic tangent
  • tangent model

That is the definition of this tangent triangle here.

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Examples

  • The slope was calculated as the tangent of the angle and then converted into appropriate units.

    Academic text (1991)
  • What this means is that the slope of our tangent line is equal to two.

  • The tangent of 1 degree is 0.017455, which corresponds to a cant of 26 mm.

    Blog text (30)
  • To calculate the exact angle, we use a simple trigonometric equation with the inverse tangent.

    Academic text (2011)
  • Students will need to be taught the algebraic and trigonometric calculations needed for polar coordinates, including the inverse tangent functions on a calculator.

    Academic text (2011)
  • To find the tangent of an angle in a right-angled triangle, divide the length of the side opposite the angle by the length of the adjacent side.

  • The teacher explained that the tangent represents a key ratio in trigonometry, particularly for calculating angles in right triangles.

Synonyms

tan
vstangent
  • Specialized
3 8.1

The opposite side divided by the adjacent side in a right triangle

is the full formal name used in standard mathematical writing

Compounds

arc tangent
  • Specialized
1 7.9

The angle whose tangent equals a given number

inverse tangent
  • Specialized
1 6.5

A math function that gives the angle whose tangent equals a number

tangent plane
  • Specialized
8.6

A flat surface that just touches a curved surface at one point

tangent curve
  • Specialized
8.1

A graph showing how tan x values change as the angle x changes

Surface Forms

tangent singular
tangents plural

Etymology

Tangent in trigonometry also comes from the Latin tangere 'to touch', because early mathematicians used a line that 'touches' a circle to define it. That's why the tangent of an angle gives a simple ratio in a right triangle: 'opposite' divided by 'adjacent'.