Find cofunction identities for all six trigonometric functions. Calculate sin↔cos, tan↔cot, sec↔csc pairs and verify complementary angle relationships.
Cofunction identities are a fundamental set of relationships in trigonometry that connect pairs of trigonometric functions through complementary angles. Two angles are complementary when they sum to 90° (or π/2 radians). The cofunction identities state that sin(θ) = cos(90° − θ), cos(θ) = sin(90° − θ), tan(θ) = cot(90° − θ), cot(θ) = tan(90° − θ), sec(θ) = csc(90° − θ), and csc(θ) = sec(90° − θ). These relationships are essential in simplifying trigonometric expressions, solving equations, and proving other identities.
Our cofunction calculator lets you enter any angle in degrees or radians and instantly see all six trigonometric function values alongside their cofunction counterparts. The tool verifies each identity by calculating both sides independently and comparing results. Whether you are studying for a precalculus exam, working through homework problems, or need to quickly look up cofunction pairs for an engineering application, this calculator provides accurate results with customizable decimal precision. Presets for common angles like 30°, 45°, and 60° let you explore standard values quickly, while the comparison bars give you an intuitive visual of how function and cofunction values relate.
Cofunction Calculator helps you solve cofunction problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter Angle, Decimal Places once and immediately inspect Angle (degrees), Complement (90° − θ), Angle (radians) to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
sin(θ) = cos(90° − θ), cos(θ) = sin(90° − θ), tan(θ) = cot(90° − θ), cot(θ) = tan(90° − θ), sec(θ) = csc(90° − θ), csc(θ) = sec(90° − θ)
Result: Angle (degrees) shown by the calculator
Using the preset "30°", the calculator evaluates the cofunction setup, applies the selected algebra rules, and reports Angle (degrees) with supporting checks so you can verify each transformation.
This calculator takes Angle, Decimal Places and applies the relevant cofunction relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use Angle (degrees), Complement (90° − θ), Angle (radians), Complement (radians) to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
A cofunction is the trigonometric function of the complementary angle. For any angle θ, sin(θ) and cos(90°−θ) are cofunctions of each other, as are tan/cot and sec/csc.
The prefix "co-" comes from "complementary." Cosine literally means "complement's sine," cotangent means "complement's tangent," and cosecant means "complement's secant."
Yes. The identities sin(θ) = cos(90°−θ) hold for all real values of θ, not just acute angles. The complement (90°−θ) may be negative or greater than 90° but the identity remains valid.
They appear frequently when differentiating and integrating trig functions. For example, d/dx[sin x] = cos x, and cofunction identities help convert between forms when simplifying integrals.
The cofunction is cot(90°−45°) = cot(45°) = 1. Since 45° is its own complement, tan(45°) = cot(45°) = 1.
Yes. If sin(2x) = cos(3x), you can write cos(90°−2x) = cos(3x), giving 90°−2x = 3x, so x = 18°. Cofunction substitution often simplifies trig equations.