Enter an angle in degrees or radians and the Secant Calculator returns the sec(α) value instantly. The secant is the reciprocal of cosine — sec(x) = 1/cos(x) — making this tool useful for trigonometry, geometry, and engineering problems. Choose your angle unit, type in the value, and get the secant result along with the corresponding cosine for reference.
sec(α)
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cos(α)
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Angle in Degrees
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Angle in Radians
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The secant (sec) is a trigonometric function defined as the reciprocal of the cosine: sec(x) = 1/cos(x). In a right triangle, it equals the ratio of the hypotenuse to the adjacent side. It is an even function, meaning sec(-x) = sec(x).
You can use either degrees or radians with the secant function — just make sure to be consistent. Most scientific calculators default to radians. This calculator lets you choose your preferred unit. To convert degrees to radians, multiply by π/180.
Yes. Since secant is an even function, sec(-α) = sec(α). This mirrors the behavior of the cosine function, which is also even. So sec(-45°) equals sec(45°).
The secant function is undefined wherever cosine equals zero, which occurs at x = π/2 + πn (i.e., 90°, 270°, 450°, etc.) for any integer n. At these angles, sec(x) approaches ±infinity. The range of secant is (-∞, -1] ∪ [1, ∞).
Most calculators don't have a dedicated secant button. To find sec(x), first calculate cos(x) using your calculator's cosine function, then take its reciprocal: sec(x) = 1 ÷ cos(x). Make sure your calculator is set to the correct angle mode (degrees or radians).
Yes, for common angles you can use known cosine values. For example, cos(60°) = 0.5, so sec(60°) = 1/0.5 = 2. For cos(45°) = √2/2, sec(45°) = √2 ≈ 1.4142. Memorizing key cosine values lets you derive secants mentally.
Secant (sec) takes an angle as input and returns a ratio. Arccosine (arccos or cos⁻¹) is the inverse cosine function — it takes a ratio as input and returns an angle. They are related but not the same: sec(x) = 1/cos(x), while arccos is the inverse of cosine itself.
Some frequently used values: sec(0°) = 1, sec(30°) ≈ 1.1547, sec(45°) = √2 ≈ 1.4142, sec(60°) = 2, sec(90°) is undefined. These values repeat with sign changes across the full 360° cycle.