cotangent

American  

[koh-tan-juhnt, koh-tan-] / koʊˈtæn dʒənt, ˈkoʊˌtæn- /

Also cotan

noun

Trigonometry.

1. (in a right triangle) the ratio of the side adjacent to a given angle to the side opposite.

2. the tangent of the complement, or the reciprocal of the tangent, of a given angle or arc. cot, ctn

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cotangent British  

/ ˌkəʊtænˈdʒɛnʃəl, kəʊˈtændʒənt /

noun

1. Abbreviation: cot.   cotan.   ctn.  (of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the adjacent side to that of the opposite side; the reciprocal of tangent

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cotangent Scientific  

/ kō-tăn′jənt /

1. The ratio of the length of the adjacent side of an acute angle in a right triangle to the length of the opposite side. The cotangent is the inverse of the tangent.

2. The ratio of the ordinate to the abscissa of the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.

3. A function of a number x, equal to the cotangent of an angle whose measure in radians is equal to x.

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Other Word Forms

• cotangential adjective

Etymology

Origin of cotangent

First recorded in 1625–35, cotangent is from the New Latin word cotangent- (stem of cotangēns ). See co-, tangent

Example Sentences

Then, we can find the other trigonometric functions easily because we know that the reciprocal of sine is cosecant, the reciprocal of cosine is secant, and the reciprocal of tangent is cotangent.

From Textbooks • Dec. 1, 2021

Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd.

From Textbooks • Feb. 13, 2015

The secant, cotangent, and cosecant are all reciprocals of other functions.

From Textbooks • Feb. 13, 2015

Where the graph of the tangent function increases, the graph of the cotangent function decreases.

From Textbooks • Feb. 13, 2015

The cotangent graph has vertical asymptotes at each value of where we show these in the graph below with dashed lines.

From Textbooks • Feb. 13, 2015