Calculate cosecant with csc

csc(x) returns the cosecant of x, defined as 1 / sin(x). It is the reciprocal trigonometric function used when a formula naturally contains inverse sine ratios.

Examples and connections

csc(pi / 2) is 1. Use sin for the direct ratio and cot for another reciprocal-family function. The identity csc(x)^2 = 1 + cot(x)^2 is useful for checking algebraic transformations.

Domain caution

Cosecant is undefined whenever sine is zero, including integer multiples of pi. It grows without bound near those points, so values near a pole are sensitive to rounded angles. Use pi to express exact radian angles and round only for display.

Choosing the right function

In many numerical applications, calculating sine then dividing explicitly makes domain handling clearer. Csc is concise in symbolic formulas. Its inverse counterpart is acsc; principal-value conventions mean it will not return every possible angle sharing a cosecant.