cosecant
the reciprocal of the sine function. The ratio of the hypotenuse/opposite or r/y in a right triangle
Cosecant (csc) is one of the trigonometric functions which is defined as the reciprocal of the sine function. In other words, csc(theta) gives the ratio of the length of the hypotenuse of a right triangle to the length of the opposite side of the angle theta. Cosecant is used in trigonometry to calculate angles and distances in triangles.
The formula for cosecant is:
csc(theta) = 1 / sin(theta)
The range of csc(theta) is (-infinity, -1] U [1, +infinity), which means that the value of csc(theta) can be any real number except zero.
Cosecant has several important properties that make it useful in trigonometry. For example, the reciprocal identity states that:
csc(theta) = 1 / sin(theta)
Another important property is that csc(theta) is an odd function, which means that:
csc(-theta) = -csc(theta)
Moreover, the periodicity of csc(theta) is 2pi.
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