# Documentation/Calc Functions/CSC

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CSC

Mathematical

## Summary:

Calculates the trigonometric cosecant (csc) of an angle expressed in radians.

CSC(Number)

## Returns:

Returns a number that is the trigonometric cosecant of the specified angle. The value returned is a real number x, such that x ≤ -1 or x ≥ 1 (x cannot lie in the range (-1, 1)).

## Arguments:

Number is a real number, or a reference to a cell containing that number, that is the angle in radians whose trigonometric cosecant is to be calculated.

• If Number is non-numeric, then CSC reports a #VALUE! error.
• If Number is equal to 0, then CSC reports a #NUM! error.

If your angle is expressed in degrees, either multiply by PI()/180 or use the RADIANS function to convert to radians.

The formula for the trigonometric cosecant of x is:

$\displaystyle{ \text{csc}(x)~=~\frac{1}{\sin(x)} }$

Mathematically, the cosecant of any integer multiple of π, i.e. {......-2π, -π, 0, π, 2π.....} is undefined. For this reason, CSC reports an error when its argument is equal to 0. However, because of the inherent inaccuracy in representing π numerically, CSC does not report errors for other argument values. You should be aware that CSC will return large positive or negative results for non-zero integer values of π.

The figure below illustrates the function CSC.

## Examples:

Formula Description Returns
=CSC(1) Trigonometric cosecant of 1 radian. 1.18839510577812
=CSC(D1) where cell D1 contains the number -0.5. Trigonometric cosecant of -½ radian. -2.08582964293349
=CSC(PI()/4) Trigonometric cosecant of π/4 radians. 1.4142135623731
=CSC(RADIANS(30)) Trigonometric cosecant of 30°, after first converting the angle from degrees to radians. 2

CSC