Enter an angle and select a trigonometric function (sin, cos, tan, cot, sec, or csc) to find its cofunction — the complementary trig function evaluated at 90° minus your angle. The Cofunction Calculator returns the cofunction identity, the complementary angle, and the numeric result for both the original and cofunction values.
Cofunction Result
--
Original Function Value
--
Complementary Angle (Degrees)
--
Complementary Angle (Radians)
--
A cofunction is a trigonometric function that is related to another trig function through complementary angles (angles that sum to 90°). The cofunction pairs are: sin & cos, tan & cot, and sec & csc. For any angle x, f(x) equals the cofunction of its complement (90° − x).
The six cofunction identities are: sin(x) = cos(90° − x), cos(x) = sin(90° − x), tan(x) = cot(90° − x), cot(x) = tan(90° − x), sec(x) = csc(90° − x), and csc(x) = sec(90° − x). To use them, simply substitute your angle into the complementary function evaluated at 90° minus that angle.
Using the cofunction identity sin(x) = cos(90° − x), we set 90° − x = 15°, which gives x = 75°. So sin(75°) = cos(15°).
Use the identity sin(x) = cos(90° − x). For example, sin(40°) = cos(50°). Just subtract the angle from 90° and evaluate the cosine of the result. The two values will be equal.
In radians, the complement of angle x is π/2 − x (since 90° = π/2 radians). So the cofunction identities in radians become: sin(x) = cos(π/2 − x), tan(x) = cot(π/2 − x), and sec(x) = csc(π/2 − x).
The cofunction of tangent is cotangent. So tan(90° − x) = cot(x). This means that the tangent of a complementary angle equals the cotangent of the original angle, and vice versa.
The cofunction of cosecant (csc) is secant (sec). The identity is csc(x) = sec(90° − x). Conversely, sec(x) = csc(90° − x). These functions are cofunctions because they are defined as the reciprocals of sin and cos respectively, which are themselves cofunctions.
Cofunction identities simplify trigonometric calculations by letting you convert between function pairs using complementary angles. They are especially useful in solving equations, simplifying expressions, and understanding symmetry in the unit circle. Engineers and physicists frequently use them when analyzing wave behavior and phase relationships.