Cofunction Calculator
Calculate trigonometric cofunctions and complementary angles
How to Use This Calculator
Enter the Angle
Input the angle value you want to calculate cofunctions for. You can use degrees or radians.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad).
Calculate
Click "Calculate Cofunctions" to see all trigonometric functions and their cofunction relationships.
Review Results
See the complementary angle and verify that each function equals its cofunction evaluated at the complementary angle.
Formula
Cofunction Identities
Basic Cofunction Identities:
- 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)
Complementary Angles:
Two angles are complementary if their sum is 90° (π/2 radians). For angle θ, its complement is (90° - θ) or (π/2 - θ).
Key Relationships:
- Sine and cosine are cofunctions of each other
- Tangent and cotangent are cofunctions of each other
- Secant and cosecant are cofunctions of each other
- Each function evaluated at an angle equals its cofunction evaluated at the complementary angle
About Cofunction Calculator
The Cofunction Calculator is a specialized tool that demonstrates and calculates trigonometric cofunction identities. Cofunctions are pairs of trigonometric functions that are related through complementary angles. Understanding cofunctions is essential for simplifying trigonometric expressions and solving trigonometric equations.
What are Cofunctions?
Cofunctions are pairs of trigonometric functions that have special relationships. The key concept is that if two angles are complementary (sum to 90°), then the trigonometric function of one angle equals the cofunction of the other angle. For example, sin(30°) = cos(60°) because 30° and 60° are complementary.
When to Use This Calculator
- Trigonometric Simplification: Simplify expressions using cofunction identities
- Verification: Verify cofunction relationships for any given angle
- Learning: Understand the complementary nature of trigonometric functions
- Problem Solving: Use cofunction identities to solve trigonometric equations
- Homework Help: Check your work when using cofunction identities
Why Use Our Calculator?
- ✅ Complete Results: Shows all six trigonometric functions and their cofunctions
- ✅ Complementary Angle: Automatically calculates and displays the complementary angle
- ✅ Visual Relationships: Clearly shows which functions are cofunctions
- ✅ Multiple Units: Supports both degrees and radians
- ✅ 100% Free: No registration or payment required
- ✅ Educational: Helps understand fundamental trigonometric relationships
Cofunction Pairs
- Sine and Cosine: sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ)
- Tangent and Cotangent: tan(θ) = cot(90° - θ) and cot(θ) = tan(90° - θ)
- Secant and Cosecant: sec(θ) = csc(90° - θ) and csc(θ) = sec(90° - θ)
Frequently Asked Questions
What are cofunctions?
Cofunctions are pairs of trigonometric functions that are related through complementary angles. If two angles add up to 90° (or π/2 radians), then the trigonometric function of one angle equals the cofunction of the other.
Why is sin(30°) = cos(60°)?
Because 30° and 60° are complementary angles (they add up to 90°). According to cofunction identities, sin(θ) = cos(90° - θ). So sin(30°) = cos(90° - 30°) = cos(60°).
What's the difference between complementary and supplementary angles?
Complementary angles add up to 90° (used for cofunctions), while supplementary angles add up to 180°. Cofunction identities only work with complementary angles.
How do I use cofunction identities to simplify expressions?
If you have a trigonometric function with an angle close to 90°, you can rewrite it using its cofunction. For example, sin(80°) = cos(10°), which might be easier to calculate or work with.
Do cofunction identities work in radians?
Yes! Just replace 90° with π/2. For example, sin(θ) = cos(π/2 - θ) and cos(θ) = sin(π/2 - θ).
Can I use cofunctions for angles greater than 90°?
The cofunction identities work for any angle, but they're most useful when working with complementary pairs. For angles greater than 90°, you can still use the identities, but you'll need to consider the quadrant and sign of the function values.