Excel SEC Function

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

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:

Images courtesy of wumbo.net.