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Excel CSC Function

Excel CSC function
Summary 
The Excel CSC function returns the cosecant of an angle provided in radians.
Purpose 
Get cosecant of an angle
Return value 
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Syntax 
=CSC (number)
Arguments 
  • number - The angle provided in radians.
Usage notes 

The CSC function returns the cosecant of an angle provided in radians. In geometric terms, the cosecant of an angle is equal to the ratio of a right triangle's hypotenuse divided by its opposite side. For example, the cosecant of PI()/6 or 30° returns the ratio 2.0.

=CSC(PI()/6) // Returns 2.0

Using Degrees

The CSC function expects radians. To supply an angle to CSC in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians. For example, to get the CSC of 60 degrees, you can use either formula below:

=CSC(60*PI()/180)
=CSC(RADIANS(60))

Explanation

Graph of Cosecant Function

The graph of cosecant, shown above, visualizes the output of the function for angles from 0 to a full rotation. The function has vertical asymptotes within the range  [0, 2π] at the points 0, π and 2π where the output diverges to infinity. CSC is the inverse of SIN and can be equivalently defined in the formula below:

=CSC(angle)=1/SIN(angle)

The relationship between cosecant and sine is visualized by the graph of the two functions shown below:

Graph of Cosecant and Sine Function

Graphs courtesy of wumbo.net.