What is a cofunction in trigonometry?

A cofunction is a trigonometric function paired with another such that they share equal values when their angles are complementary — meaning the angles sum to 90°. The three pairs are sine and cosine, tangent and cotangent, and secant and cosecant. For example, sin(30°) equals cos(60°) because 30° and 60° are complementary, summing to 90°.

What are the six cofunction identities?

The six cofunction identities are: 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). In radian form, replace 90° with π/2. These identities hold for all real values of θ where the functions are defined, enabling bidirectional conversion within each pair.

How do you use a cofunction identity to find cos(20°)?

Apply the identity cos(θ) = sin(90° − θ) with θ = 20°: cos(20°) = sin(90° − 20°) = sin(70°) ≈ 0.9397. This approach proves especially useful when a reference table provides sine values but not cosine values, enabling seamless conversion between the two functions using only the complementary-angle relationship.

What is the cofunction of sin(45°)?

The cofunction of sin(45°) is cos(90° − 45°) = cos(45°) = √2/2 ≈ 0.7071. Because 45° is its own complement — it satisfies 45° + 45° = 90° — sine and cosine are exactly equal at this angle. This self-complementary property makes 45° a frequently cited benchmark angle in geometry, physics, and engineering problems.

Does the cofunction calculator support radian inputs?

Yes, the cofunction calculator fully supports radian inputs. When radian mode is selected, the complementary angle is computed as π/2 − θ instead of 90° − θ. For example, entering θ = π/6 radians with the sine function computes sin(π/6) = cos(π/2 − π/6) = cos(π/3) = 0.5, which is identical to the degree-mode result for 30°, confirming unit-independent accuracy.

Why are cofunction identities important in mathematics and applied science?

Cofunction identities simplify complex trigonometric expressions, reduce redundant computations, and reveal symmetry between function pairs. In calculus, they appear in integration by substitution and Fourier series analysis. In electrical engineering, they describe the 90° phase relationship between sine and cosine waveforms modeling AC voltage and current. Mastering these identities accelerates equation-solving, proof construction, and real-world modeling tasks across every STEM discipline.

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Cofunction Calculator

Calculate cofunction values for sin, cos, tan, cot, sec, and csc using complementary angle identities. Supports degrees and radians.

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Angle (θ)

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Cofunction Value

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