Secant Calculator
Cosine's Reciprocal
Secant flips cosine upside down: one divided by cos(θ). Like the other reciprocal trig functions, it isn't part of the "big three" taught first, but it appears naturally in calculus (the derivative of tangent involves sec²) and in any geometry problem where a formula is more directly expressed with cosine in the denominator.
The Formula
sec(θ) = 1 / cos(θ)
Secant is undefined wherever cosine equals zero — at 90° and 270°, and every 180° from those points. The calculator checks for a near-zero cosine value and returns an explicit error there instead of an unstable result.
Where Secant Appears
- Calculus — the derivative of tan(θ) is sec²(θ), making secant a recurring term in trigonometric integration and differentiation.
- Optics and lens design — certain angle-of-incidence formulas are expressed using secant directly.
- Surveying — secant-based formulas appear in specific triangulation methods.
| Angle | sec(θ) |
|---|---|
| 0° | 1 |
| 30° | 1.154701 |
| 45° | 1.414214 |
| 60° | 2 |
How to Use This Calculator
- Enter the Angle.
- Select the unit: Degrees or Radians.
- Select Calculate to see the secant value.
Related Calculations
Secant is the reciprocal of the Cosine Calculator. See also the Cosecant Calculator for sine's reciprocal.