Cosecant Function: Definition, Formula, Graph and Properties Explained

csc(x)

: -csc(x)cot(x)

csc(x) is a trigonometric function, also known as the cosecant function. It is defined as the reciprocal of the sine function and is given by the following formula:

csc(x) = 1/sin(x)

In other words, the cosecant of an angle x is the ratio of the length of the hypotenuse of a right triangle to the length of the opposite side of the triangle, where x is one of the acute angles in the triangle.

The values of csc(x) range from negative infinity to positive infinity and the function is undefined at values of x where sin(x) = 0. Therefore, the function has vertical asymptotes at x = nπ, where n is an integer.

csc(x) is an odd function, which means that it has rotational symmetry about the origin. Its graph resembles a series of curves that approach vertical asymptotes at x = nπ and oscillate between positive and negative values as x increases or decreases. The period of csc(x) is 2π.

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