What is the secant function?

Secant is defined as sec(θ) = 1 / cos(θ). It is one of the six standard trigonometric functions and is the reciprocal of cosine.

When is secant undefined?

Secant is undefined whenever cos(θ) = 0, which occurs at odd multiples of 90° (i.e., 90°, 270°, −90°, …) or π/2 radians and its odd multiples. Division by zero is not a real number.

How do I convert degrees to radians?

Multiply degrees by π / 180. For example, 60° × (π / 180) ≈ 1.0472 radians. The calculator does this conversion automatically when you select the degree mode.

What is the range of the secant function?

The range of sec(θ) is (−∞, −1] ∪ [1, +∞). Secant can never return a value strictly between −1 and 1.

Is sec(θ) the same as arccos(θ)?

No. sec(θ) = 1 / cos(θ) is the reciprocal of cosine. arccos(θ) is the inverse cosine function — these are completely different operations.

How accurate are the results?

Results use JavaScript's built-in Math.cos(), which follows IEEE 754 double-precision floating-point arithmetic. Values are displayed to 10 decimal places.

Secant Calculator

Enter an angle in degrees or radians to instantly compute its secant value (1 / cos θ).

Angle Input

Angle

Unit

Degrees Radians

Common angles

Result

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Enter an angle to compute sec(θ)

Formula: sec(θ) = 1 / cos(θ) | Range: (−∞, −1] ∪ [1, +∞) | Undefined when cos(θ) = 0

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Summary

The secant function is the reciprocal of cosine: sec(θ) = 1 / cos(θ). This calculator accepts any angle in degrees or radians, converts it as needed, and returns the secant value rounded to ten decimal places. Angles where cos(θ) = 0 — such as 90° or 270° — are undefined and flagged automatically.

How it works

Enter an angle value in the input field.
Select whether the angle is in degrees or radians.
Click Calculate (or press Enter) to compute the result.
The tool evaluates cos(θ) and returns 1 / cos(θ) as the secant.
Step-by-step working is displayed below the result for verification.
Switch units at any time — the angle is converted automatically.

Use cases

Verify manual trigonometry calculations for homework or exams.
Compute secant values when a calculator only has a cos button.
Explore behavior of sec(θ) near undefined points (±90°, ±270°).
Cross-check results from engineering or physics formulas that use sec.
Convert between degree and radian inputs on the fly.
Understand secant graphically using the step-by-step breakdown.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu