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The Art of Interface |
Article 11 — Appendix A.25sec trigonometric secant functionCategory. Mathematics. Abstract. Trigonometric secant: definition, graph, properties, identities and table of values for some angles. References. This article is a part of scientific calculator Li-L, scientific calculator Li-X, scientific calculator Li-Lc and scientific calculator Li-Xc products. 1. DefinitionSecant of the angle is ratio of the hypotenuse to adjacent leg. 2. GraphSecant is 2π periodic function defined everywhere on real axis, except its singular points π/2 + πn, n=0, ±1, ±2, ... — so, function domain is (−π/2 + πn, π/2 + πn), n∈N. Its stalactite-stalagmite graph is depicted below — fig. 1. ![]() Function codomain is entire real axis with gap in the middle: (−∞, −1]∪[1, +∞). 3. IdentitiesBase: csc−2φ + sec−2φ = 1and its consequences: secφ = ±1 /√(1 − sin2φ)secφ = ±√(1 + tan2φ) secφ = ±√(1 + cot2φ) / cotφ secφ = ±cscφ /√(csc2φ − 1) By definition: secφ ≡ 1 /cosφProperties symmetry, periodicity, etc.: sec−φ = cscφsecφ = sec(φ + 2πn), where n = 0, ±1, ±2, ... secφ = −sec(π − φ) secφ = −sec(π + φ) secφ = csc(π/2 + φ) Sum of angles: sec(φ + ψ + χ) = secφ secψ secχ / (1 − tanφ tanψ − tanφ tanχ − tanψ tanχ)Some angles:
4. SupportTrigonometric secant function sec is supported in: Trigonometric secant function of the complex argument sec is supported in:
5. How to useTo calculate secant of the number:
To calculate secant of the current result:
To calculate secant of the angle φ in memory:
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