Purpose
Return value
Syntax
=SEC(number)
- number - The angle in radians for which you want the secant.
Using the 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 .
Purpose
Return value
Syntax
=SECH(number)
- number - The hyperbolic angle.
Using the SECH function
The Excel SECH function returns the hyperbolic secant of a hyperbolic angle angle. Given 2 as input, the function returns 0.265802229 as output.
=SECH(2) // returns 0.265802229
Explanation
The hyperbolic secant is the reciprocal of the COSH function.
=1/COSH(x) // equivalent to SECH(x)
The plot below show’s the function’s output in Excel.
