Secant Calculator
Calculate the secant of any angle. Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).
Results
sec(θ)
1.154701
Angle (radians)
0.523599 rad
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Secant Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.
Review your inputs
Double-check that all values are correct and match the units or format shown for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Secant Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
When to Use This Calculator
- •Use the Secant Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
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About Secant Calculator
The secant function is the reciprocal of the cosine function: sec(θ) = 1/cos(θ). In a right triangle, it equals the ratio of the hypotenuse to the adjacent side. Secant is undefined at 90° and 270° (where cosine equals zero) and has a minimum absolute value of 1. The secant function has a period of 360° (2π radians) and is an even function: sec(−θ) = sec(θ). While secant is less commonly used in everyday calculations than sine, cosine, or tangent, it plays an important role in calculus, particularly in integration and trigonometric substitution. The integral of secant, ∫ sec(x) dx = ln|sec(x) + tan(x)| + C, is historically significant and was one of the key results needed for the Mercator map projection. This calculator computes the secant for any angle.
The Math Behind It
Formula Reference
Secant Function
sec(θ) = 1 / cos(θ) = hypotenuse / adjacent
Variables: θ = angle
Worked Examples
Example 1: Secant at standard angles
Compute sec(60°).
sec(60°) = 2
Common Mistakes & Tips
- !Trying to compute sec(90°) — it is undefined since cos(90°) = 0.
- !Confusing secant with cosecant — sec = 1/cos, csc = 1/sin.
- !Expecting sec(θ) to be between −1 and 1 — secant values are always |sec(θ)| ≥ 1 or undefined.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
What is the range of the secant function?
sec(θ) can take any value in (−∞, −1] ∪ [1, ∞). It is never between −1 and 1.
Why is secant important in calculus?
The identity 1 + tan²(θ) = sec²(θ) appears in many integrals, and trigonometric substitution x = a sec(θ) handles integrals involving √(x² − a²).
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