Secant Calculator
Calculate sec(x) = 1/cos(x) for any angle
Common Secant Values
0°
1
30°
2√3/3 ≈ 1.155
45°
√2 ≈ 1.414
60°
2
90°
Undefined
180°
-1
270°
Undefined
360°
1
How to Use This Calculator
Enter the Angle
Input the angle value you want to calculate the secant for. You can use degrees or radians.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad).
Calculate
Click "Calculate Secant" to get the result. Note that secant is undefined when cos(θ) = 0.
Review Results
View the secant value along with related trigonometric functions for the same angle.
Formula
sec(θ) = 1 / cos(θ)
Reciprocal of cosine
Definition:
Secant is the reciprocal of the cosine function. It's one of the six trigonometric functions and is often used in trigonometry and calculus.
Properties:
- Range: (-∞, -1] ∪ [1, ∞) - all real numbers except between -1 and 1
- Period: 360° (2π radians) - same as cosine
- Undefined: When cos(θ) = 0 (at 90°, 270°, etc.)
- Even Function: sec(-θ) = sec(θ)
Right Triangle Definition:
sec(θ) = hypotenuse / adjacent
About Secant Calculator
The Secant Calculator is a specialized tool for calculating secant values for any angle. Secant (sec) is the reciprocal of the cosine function, meaning sec(θ) = 1/cos(θ). It's one of the six fundamental trigonometric functions and is widely used in advanced mathematics, physics, and engineering applications.
What is Secant?
Secant is the reciprocal trigonometric function of cosine. In a right triangle, secant of an angle is the ratio of the hypotenuse to the adjacent side. On the unit circle, secant represents the reciprocal of the x-coordinate (since cosine is the x-coordinate).
When to Use This Calculator
- Trigonometric Calculations: Find secant values for angles in degrees or radians
- Physics Problems: Calculate values needed for wave equations and oscillations
- Engineering: Solve problems involving periodic functions and vibrations
- Mathematics: Simplify trigonometric expressions involving secant
- Verification: Verify manual calculations and check homework answers
Why Use Our Calculator?
- ✅ Instant Results: Get accurate secant values immediately
- ✅ Multiple Units: Supports both degrees and radians
- ✅ Related Functions: Shows sine, cosine, tangent, and cosecant for comparison
- ✅ Undefined Detection: Clearly indicates when secant is undefined
- ✅ Easy to Use: Simple interface for all skill levels
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works on all devices
Important Notes
- Undefined Values: Secant is undefined when cos(θ) = 0, which occurs at 90°, 270°, and their multiples
- Range: Secant values are always ≥ 1 or ≤ -1, never between -1 and 1
- Reciprocal Relationship: sec(θ) × cos(θ) = 1 (when both are defined)
Frequently Asked Questions
What is sec(0°)?
sec(0°) = 1. This is because cos(0°) = 1, and sec(θ) = 1/cos(θ), so sec(0°) = 1/1 = 1.
Why is secant undefined at 90° and 270°?
Secant is undefined when cos(θ) = 0. At 90° and 270° (and their multiples), cos(θ) = 0, so we would be dividing by zero: sec(θ) = 1/0, which is undefined.
What's the relationship between secant and cosine?
Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ). When cosine is large, secant is small, and vice versa. They multiply to 1: cos(θ) × sec(θ) = 1 (when both are defined).
Can secant be between -1 and 1?
No! Secant values are always ≥ 1 or ≤ -1, never between -1 and 1. This is because cosine values are between -1 and 1, so their reciprocals (secant) must be outside that range.
How is secant used in practice?
Secant appears in various applications including wave equations, signal processing, electrical engineering (AC circuits), and in solving certain types of differential equations.
What are the cofunction relationships for secant?
sec(θ) = csc(90° - θ). Secant and cosecant are cofunctions - the secant of an angle equals the cosecant of its complement.