Secant Calculator
Calculate the secant (sec) of any angle in degrees or radians with step-by-step explanation
Calculate Secant Function
Enter the angle for which to calculate secant
Click to set common angle values
Secant Results
Formula: sec(x) = 1/cos(x)
Input angle: 0° (0.0000 rad)
cos(0°): 1.000000
Function Analysis
Step-by-Step Calculation
Step 1: Convert to Standard Form
Given angle: 0°
Convert to radians: 0° × (π/180) = 0.000000 rad
Step 2: Calculate Cosine
cos(0.000000) = 1.000000
Exact cosine value: 1
Step 3: Calculate Secant
sec(x) = 1/cos(x)
sec(0°) = 1/1.000000
sec(0°) = 1.000000
Secant Function Properties
Domain
All real numbers except x = π/2 + kπ
Where k is any integer
Range
(-∞, -1] ∪ [1, +∞)
|sec(x)| ≥ 1
Period
2π radians (360°)
sec(x + 2π) = sec(x)
Symmetry
Even function
sec(-x) = sec(x)
Special Angle Values
Understanding the Secant Function
What is the Secant Function?
The secant function (sec) is one of the six fundamental trigonometric functions. It is defined as the reciprocal of the cosine function: sec(x) = 1/cos(x). In a right triangle, secant represents the ratio of the hypotenuse to the adjacent side.
Key Characteristics
- •sec(x) = 1/cos(x) for all x where cos(x) ≠ 0
- •Always has absolute value ≥ 1
- •Undefined when cosine equals zero
- •Has vertical asymptotes at x = π/2 + kπ
Mathematical Relationships
Basic Identity
sec(x) = 1/cos(x)
Pythagorean Identity
sec²(x) - tan²(x) = 1
Even Function Property
sec(-x) = sec(x)
Note: The secant function is undefined at angles where the cosine is zero, creating vertical asymptotes in its graph.