The secant is the reciprocal of the cosine: hypotenuse divided by adjacent side. The identity 1 + tan²α = sec²α makes it a regular guest in calculus, and it gives slant lengths from horizontal distances.
How to use the Secant Calculator
- Angle unit
- Angle α
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter the angle and pick its unit. The angle is converted to radians and sec is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.
Formula
sec α = 1 / cos α = hypotenuse / adjacent
Range: (−∞, −1] ∪ [1, ∞) · Domain: α ≠ 90° + k·180° · Period: 2π (360°)
Worked example
Inputs — Angle unit: Degrees (°); Angle α: 30.
Results — sec(α) = 1.154700538; sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; cot(α) = 1.732050808.
Key terms
- Secant
- sec α = 1 / cos α = hypotenuse / adjacent.
- Exact value
- A value written with integers and square roots instead of decimals.
Frequently asked questions
What is sec 60°?
2, because cos 60° = 1/2.
When is secant undefined?
When cos α = 0: at 90°, 270° and so on.
Is secant even?
Yes, like cosine: sec(−α) = sec α.
What identity links secant and tangent?
1 + tan²α = sec²α.