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Calculate the secant of any angle. Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).
| Degrees | Radians | Exact Value | Decimal |
|---|---|---|---|
| 0° | 0 | 1 | 1.0000 |
| 30° | π/6 | 2√3/3 | 1.1547 |
| 45° | π/4 | √2 | 1.4142 |
| 60° | π/3 | 2 | 2.0000 |
| 90° | π/2 | undefined | — |
| 120° | 2π/3 | -2 | -2.0000 |
| 135° | 3π/4 | -√2 | -1.4142 |
| 150° | 5π/6 | -2√3/3 | -1.1547 |
| 180° | π | -1 | -1.0000 |
| 270° | 3π/2 | undefined | — |
| 360° | 2π | 1 | 1.0000 |
All θ except 90°, 270°, ...
Where cos(θ) ≠ 0
(-∞, -1] ∪ [1, ∞)
|sec(θ)| ≥ 1
2π radians (360°)
sec(θ + 2π) = sec(θ)
Even function: sec(-θ) = sec(θ)
y-axis symmetry
Secant is the reciprocal of cosine. It equals 1 divided by the cosine of the angle, or in a right triangle, hypotenuse divided by adjacent side.
Because sec(-θ) = 1/cos(-θ) = 1/cos(θ) = sec(θ). Since cosine is even, secant is also even.
Secant is undefined when cos(θ) = 0, which occurs at 90°, 270°, and odd multiples of 90°.