What are sec, cosec and cot?
They are the reciprocal trig functions: sec θ = 1/cos θ, cosec θ = 1/sin θ and cot θ = cos θ/sin θ (equivalently 1/tan θ).
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Reciprocal Trig Functions
Evaluate secant, cosecant and cotangent at any angle, with their definitions, undefined points and the working shown, in degrees or radians.
sec θ = 1/cos θ; cosec θ = 1/sin θ; cot θ = cos θ/sin θ
Angle unit
Frequently asked questions
Can you show a worked example?
sec 60° = 1/cos 60° = 1/0.5 = 2. The same angle in radians is 60° = π/3 ≈ 1.0472 rad; the toggle re-derives it in radians.
Where are they undefined?
sec and tan are undefined at 90° and 270° (cos = 0); cosec and cot are undefined at 0° and 180° (sin = 0). Their graphs have vertical asymptotes there.
How do they connect to the Pythagorean identities?
Dividing sin²+cos²=1 gives 1+tan²=sec² and 1+cot²=cosec², so the reciprocal functions appear directly in those identities.
Where are they used?
In calculus (the derivative of tan θ is sec²θ), in resolving forces, and anywhere the reciprocal of a ratio is the natural quantity.