cosecant

American  

[koh-see-kuhnt, -kant] / koʊˈsi kənt, -kænt /

noun

Trigonometry.

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

2. the secant of the complement, or the reciprocal of the sine, of a given angle or arc. csc

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cosecant British  

/ kəʊˈsiːkənt /

noun

1.  cosec.  (of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the hypotenuse to that of the opposite side; the reciprocal of sine

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cosecant Scientific  

/ kō-sē′kănt′ /

1. The ratio of the length of the hypotenuse in a right triangle to the length of the side opposite an acute angle. The cosecant is the inverse of the sine.

2. The reciprocal of the ordinate 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 cosecant of an angle whose measure in radians is equal to x.

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Etymology

Origin of cosecant

First recorded in 1700–10, cosecant is from the New Latin word cosecant- (stem of cosecāns ). See co-, secant

Example Sentences

Use the reciprocal relationship of the cosine and secant functions to draw the cosecant function.

From Textbooks • Feb. 13, 2015

The cosecant function is the reciprocal of the sine function, which means that the cosecant of a negative angle will be interpreted as The cosecant function is therefore odd.

From Textbooks • Feb. 13, 2015

Where the graph of the sine function decreases, the graph of the cosecant function increases.

From Textbooks • Feb. 13, 2015

For the four trigonometric functions, sine, cosine, cosecant and secant, a revolution of one circle, or will result in the same outputs for these functions.

From Textbooks • Feb. 13, 2015

The cosecant graph has vertical asymptotes at each value of where the sine graph crosses the x-axis; we show these in the graph below with dashed vertical lines.

From Textbooks • Feb. 13, 2015