Cosecant, Secant & Cotangent Calculator

About this calculator

Cosecant, secant and cotangent are the three reciprocal trigonometric functions: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), and cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). They carry the same information as sine, cosine and tangent but flip the ratio, which makes certain formulas — especially in calculus and integration tables — much cleaner to work with, and they are undefined exactly where their base function equals zero (csc and cot at 0°/180°, sec at 90°/270°).

Electrical engineers use secant and cosecant when working with impedance and phase-angle relationships in AC circuits, while cotangent shows up constantly in optics (Brewster's angle calculations), surveying, and in identities like 1 + cot²(θ) = csc²(θ) that simplify trigonometric equations. In calculus, the derivatives and integrals of sec and csc appear frequently enough — d/dx[tan x] = sec²x, for example — that having quick reciprocal values on hand speeds up checking work by hand.

This calculator takes an angle in degrees and returns all three reciprocal ratios at once, so you don't have to compute sine, cosine and tangent separately and invert them yourself.