SEC function

The SEC function in Excel calculates the secant of a given angle, where the angle is specified in radians. The secant of an angle is the reciprocal of the cosine of that angle:

$$\text{sec}(x) = \frac{1}{\cos(x)}$$

Syntax

=SEC(number)

Parameters

• number (required): The angle in radians for which you want the secant.

Key Points

1. Angle in Radians: The input angle must be in radians. To convert degrees to radians, use the RADIANS function:

   =SEC(RADIANS(degrees))
   

2. Domain Restrictions: The SEC function is undefined for angles where
   $\cos(x) = 0$ 

   , such as

   $\frac{\pi}{2}, \frac{3\pi}{2}, \ldots$ 

   . For these values, the function returns a #NUM! error.

3. Output: The result can be either positive or negative, depending on the angle.

Examples

1. Calculate the secant of π/3:

   =SEC(PI()/3)
   

   Result: 2

2. Calculate the secant of 45 degrees:

   =SEC(RADIANS(45))
   

   Result: 1.414213

3. Calculate the secant of -π/4:

   =SEC(-PI()/4)
   

   Result: 1.414213

4. Calculate the secant for a value in cell A1:

   =SEC(A1)
   

Errors

• #NUM!: Occurs if the input results in an undefined secant (e.g., angles where
  $\cos(x) = 0$ 

  ).

• #VALUE!: Occurs if the input is not a valid numeric value.

Related Functions

• COS: Calculates the cosine of an angle.
• SIN: Calculates the sine of an angle.
• COT: Calculates the cotangent of an angle.
• CSC: Calculates the cosecant of an angle.
• TAN: Calculates the tangent of an angle.

The SEC function is useful in trigonometry and applications involving periodic functions or waveforms.