Secant, Cosecant & Cotangent Calculator
Compute the reciprocal trig functions sec, csc, and cot.
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Reciprocals are undefined where the base function is zero
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About sec, csc, and cot
The reciprocal trig functions are simply the multiplicative inverses of sine, cosine, and tangent: csc = 1/sin, sec = 1/cos, cot = 1/tan.
They are undefined wherever the denominator is zero — for example, sec is undefined at 90° because cos(90°) = 0.
Frequently Asked Questions
What are sec, csc, and cot?▾
They are the multiplicative inverses of cos, sin, and tan: sec θ = 1/cos θ, csc θ = 1/sin θ, cot θ = 1/tan θ.
Why are these called reciprocal functions?▾
Because each is the algebraic reciprocal (1 over) one of the basic trig functions. They are useful for shortening identities and for some integration and calculus problems.
Where are sec, csc, and cot undefined?▾
sec is undefined wherever cos = 0 (e.g., 90°, 270°). csc is undefined wherever sin = 0 (e.g., 0°, 180°). cot is undefined wherever tan = 0 (same as csc).
How is cot different from 1/tan?▾
They are equivalent except at the points where tan is undefined — at θ = 90°, tan blows up, but cot is exactly 0.