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sec(θ) = 1/cos(θ) =
2
Common Angles
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View detailed breakdowns and explanations below.
📘 Definition
Secant is the reciprocal of cosine:
sec(θ) = 1/cos(θ) = hypotenuse/adjacent
It is undefined when cos(θ) = 0 (at 90°, 270°, etc.).
🎓 Key Values
- sec(0°) = 1
- sec(30°) = 2/√3 ≈ 1.155
- sec(45°) = √2 ≈ 1.414
- sec(60°) = 2
- sec(90°) = Undefined
- sec(180°) = -1
💡 Properties
- Reciprocal: sec(θ) · cos(θ) = 1
- Periodic: sec(θ + 360°) = sec(θ)
- Even Function: sec(-θ) = sec(θ)
- Range: (-∞, -1] ∪ [1, ∞)
- Derivative: d/dθ[sec(θ)] = sec(θ)tan(θ)
🚀 Applications
- Calculus: Integration techniques
- Physics: Optics and wave mechanics
- Engineering: Stress analysis
- Astronomy: Celestial calculations
⚡ Pythagorean Identity
1 + tan²(θ) = sec²(θ)
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