Cofunction Calculator
Calculate trigonometric cofunctions and complementary angle relationships with step-by-step explanations
Calculate Trigonometric Cofunctions
Cofunction Identity Results
✓ Special angle recognized: 45° and its complement 45°
Original Function
Cofunction
Cofunction Identity: sin(θ) = cos(90° - θ)
Complementary angles: 45.00° + 45.00° = 90°
Verification: Both values equal ✓ Match
All Trigonometric Values at 45.00°
Cofunction Identities Reference
| Function | Cofunction Identity | In Radians |
|---|---|---|
| sin(θ) | cos(90° - θ) | cos(π/2 - θ) |
| cos(θ) | sin(90° - θ) | sin(π/2 - θ) |
| tan(θ) | cot(90° - θ) | cot(π/2 - θ) |
| cot(θ) | tan(90° - θ) | tan(π/2 - θ) |
| sec(θ) | csc(90° - θ) | csc(π/2 - θ) |
| csc(θ) | sec(90° - θ) | sec(π/2 - θ) |
What are Cofunctions?
Cofunctions are pairs of trigonometric functions whose values are equal for complementary angles.
Two angles are complementary if they add up to 90° (or π/2 radians).
The cofunction pairs are:
- • sin and cos
- • tan and cot
- • sec and csc
Special Angle Pairs
Note: At 45°, sine and cosine are equal, demonstrating the cofunction relationship.
Key Properties
Complementary angles sum to 90°
Cofunctions have equal values at complementary angles
Valid for angles 0° ≤ θ ≤ 90°
Used to simplify trigonometric expressions
Quick Tips
sin(30°) = cos(60°) = 0.5
tan(45°) = cot(45°) = 1
Use cofunctions to find unknown values
Helpful for triangle solving
Understanding Cofunction Identities
What are Cofunction Identities?
Cofunction identities are trigonometric relationships that show how certain trigonometric functions are related through complementary angles. Two angles are complementary if their sum equals 90° (or π/2 radians).
The Three Cofunction Pairs
- •Sine and Cosine: sin(θ) = cos(90° - θ)
- •Tangent and Cotangent: tan(θ) = cot(90° - θ)
- •Secant and Cosecant: sec(θ) = csc(90° - θ)
Why Do Cofunctions Work?
In a right triangle, if one acute angle is θ, the other acute angle must be (90° - θ). The trigonometric ratios for these complementary angles create the cofunction relationships.
Practical Applications
Navigation
Converting between different angle measurements
Engineering
Simplifying complex trigonometric calculations
Mathematics
Solving trigonometric equations and identities
Example: Finding cos(30°) using sin(60°)
Since 30° and 60° are complementary angles (30° + 60° = 90°), we can use the cofunction identity:
cos(30°) = sin(90° - 30°) = sin(60°)
Both values equal approximately 0.866, demonstrating the cofunction relationship.