Exceljet

Quick, clean, and to the point

Excel SEC Function

Excel SEC function
Summary 
The Excel SEC function returns the secant of an angle provided in radians.
Purpose 
Get secant of an angle
Return value 
The secant value.
Syntax 
=SEC (number)
Arguments 
  • number - The angle in radians for which you want the secant.
Version 
Usage notes 

The SEC function returns the secant of an angle provided in radians. In geometric terms, the secant of a right-triangle's angle is equal to the ratio of the length of its hypotenuse over the length of its adjacent side. For example, the secant of PI()/6 (30°) returns the ratio 1.514.

=SEC(PI()/6) // Returns 1.514

Using Degrees

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

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

Explanation

Graph of Secant Function

The graph of SEC, shown above, visualizes the output of the function for angles from 0 to a full rotation. The function has two vertical asymptotes at π/2 and 3π/2 respectively where the output of the function diverges to infinity. The SEC function is the reciprocal of COS  and can be equivalently defined in the formula below:

=SEC(angle)=1/COS(angle)

The relationship between SEC and COS is visualized in the graph of both of the functions shown below:

Graph of Secant and Cosine Function

Images courtesy of wumbo.net.

Download 200+ Excel Shortcuts

Get over 200 Excel shortcuts for Windows and Mac in one handy PDF.