Cofunction Calculator

Cofunction identities are one of the cleanest bridges between geometry and algebra in trigonometry. They say that certain trigonometric functions become each other when the angle is replaced by its complement. In plain language, the sine of an angle equals the cosine of the angle needed to complete a right angle, the tangent of an angle equals the cotangent of its complement, and the secant of an angle equals the cosecant of its complement. Written symbolically, sin(θ) = cos(90° − θ), tan(θ) = cot(90° − θ), and sec(θ) = csc(90° − θ), with the same idea holding in radians as π/2 − θ. This calculator automates those identities so you can check values instantly and see the matching cofunction side by side. The reason the identities work comes directly from right-triangle structure. In a right triangle, the two acute angles always add to 90°. The side opposite one acute angle is the side adjacent to the other, so the ratio definitions swap roles. Because sine is opposite over hypotenuse and cosine is adjacent over hypotenuse, they match across complementary angles. The same swap explains tangent and cotangent, as well as secant and cosecant. Once you see that side relationships are mirrored, the cofunction pattern becomes natural rather than mysterious. This tool lets you work in either degrees or radians, which is important because trigonometry appears in school math, engineering, physics, graphics, navigation, and signal processing. In degree mode, the complementary angle is computed as 90° minus the entered angle. In radian mode, it is computed as π/2 minus the entered angle. The calculator evaluates the original function and the paired cofunction numerically so you can compare them directly. Small differences in displayed decimals can come from floating-point rounding, but mathematically the identity is exact wherever both expressions are defined. Domain restrictions matter too. Tangent and secant are undefined whenever cosine is zero, which happens at 90° + n·180° or π/2 + nπ. Cotangent and cosecant are undefined whenever sine is zero, which happens at n·180° or nπ. The calculator checks those cases and warns you instead of displaying misleading values. Use it to verify homework, build intuition for complementary angles, prepare lessons, or quickly confirm trig identities during technical work.