🌞 Sun-browned skin 🟫 A light brown 🟫 Light brown color 🌞 To get sun-brown 👞 To make leather 📐 A math ratio

tan

3 8.1

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

noun
/tæn/

Specialized

: tangente

In our example, the adjacent side is 5 and the opposite side is 3.5. Tan(?) = Opp/Adj = Tan-1(Opp/Adj) = Tan-1(3.5/5) = Tan-1(0.7) = 34.992

The derivative of secant X is secant X times tangent X, secant X tan X.

Examples

F is same as tan alpha measured on this triangle.
Because otherwise there's no apparent way to just figure out what the derivative of our tan of X is.
You'd have to solve tan X = X.
So we're just left with tan squared X and DX.
So we know that X is tan Theta or tan Theta is equal to X.
Because all the slanted red arrows in the figure make an angle of tan-1(v/c) with the vertical, one can readily confirm that x = vt, the correct law for inertial motion.

Academic text (2012)
In a right-angled triangle, the tan of an angle is calculated by dividing the length of the opposite side by the length of the adjacent side.
To find the value of tan in trigonometry, you need to refer to the ratio for the specific angle.
When studying angles in mathematics, the tan function helps us understand the relationships between the sides of triangles.

Synonyms

tangent

vstan

Specialized

1 7.2

A ratio of the side opposite an angle to the side next to it in a right triangle

is the shortened form used in trigonometry rather than the full name

Idioms

to tan someone's hide

Archaic

9.5

To punish someone very harshly, often by hitting or scolding them

Compounds

Black and Tan

1 9.9

A member of a British force who helped the police in Ireland to stop the independence movement, 1919–1921

fan tan

1 9.9

A Chinese gambling game where players bet on how many counters remain under a bowl after grouping them by four

black and tan

5.6

A drink made by pouring dark beer over pale beer so two layers stay separate

black-and-tan

4.3

A pattern of black and tan colors on an animal's fur, often on dogs

black-and-tan coonhound

7.5

A large strong American hunting dog with black fur and tan marks that hunts raccoons

black-and-tan terrier

7.5

A small short-haired dog with black and tan fur used to hunt rats

farmer's tan

Informal

7.8

A dark mark on the skin showing where clothing does not cover you in the sun

Surface Forms

tan singular

tans plural

Etymology

The math word tan is short for tangent, a word that comes from a Latin word meaning 'touching'. In geometry a tangent line 'touches' a circle, and tan (short for tangent) became the name for the trig ratio linked to that touching line and angles.