What Is a Cofunction?
In trigonometry, a cofunction is a trigonometric function whose value for the complement of an angle equals the value of another function for that angle. Two functions are cofunctions if f(θ) = g(90° − θ).
The six trigonometric functions form three cofunction pairs:
- sin and cos — sine and cosine
- tan and cot — tangent and cotangent
- sec and csc — secant and cosecant
Cofunction Identities
For any angle θ, the six cofunction identities are:
| Identity | In Radians |
|---|---|
| sin(θ) = cos(90° − θ) | sin(θ) = cos(π/2 − θ) |
| cos(θ) = sin(90° − θ) | cos(θ) = sin(π/2 − θ) |
| tan(θ) = cot(90° − θ) | tan(θ) = cot(π/2 − θ) |
| cot(θ) = tan(90° − θ) | cot(θ) = tan(π/2 − θ) |
| sec(θ) = csc(90° − θ) | sec(θ) = csc(π/2 − θ) |
| csc(θ) = sec(90° − θ) | csc(θ) = sec(π/2 − θ) |
How to Use the Cofunction Calculator
- Select your angle unit — degrees (°) or radians (rad).
- Enter the angle θ in the input field, or tap a quick-angle button (0°, 30°, 45°, 60°, 90°).
- Click Calculate. The calculator instantly shows:
- The complement angle (90° − θ)
- All six cofunction identity pairs
- All six trig values for θ and for 90° − θ
Example: Using the Cofunction Calculator
Suppose θ = 30°. The complement is 90° − 30° = 60°.
- sin(30°) = 0.5 ⟶ cos(60°) = 0.5 ✓
- cos(30°) ≈ 0.866 ⟶ sin(60°) ≈ 0.866 ✓
- tan(30°) ≈ 0.577 ⟶ cot(60°) ≈ 0.577 ✓
Degrees vs. Radians
The cofunction identities work in both angle measurement systems:
- Degrees — commonly used in everyday contexts and US customary units. The complement of angle θ° is (90 − θ)°.
- Radians — the SI unit used in scientific and mathematical calculations. The complement of angle θ rad is (π/2 − θ) rad.
Both systems give identical results for the trig function values.
Frequently Asked Questions
- What is the cofunction of sin?
- The cofunction of sine is cosine: sin(θ) = cos(90° − θ).
- What is the cofunction of tan?
- The cofunction of tangent is cotangent: tan(θ) = cot(90° − θ).
- What is the cofunction of sec?
- The cofunction of secant is cosecant: sec(θ) = csc(90° − θ).
- Why are sin and cos called cofunctions?
- The prefix "co-" comes from "complement." Since the two acute angles of a right triangle are complementary (sum to 90°), the sine of one angle equals the cosine of the other — hence "cosine" means "complement's sine."
- Do cofunction identities work for angles greater than 90°?
- Yes. The identities hold for all real angles, not just acute ones, because the complement 90° − θ can be negative or obtuse.