Trigonometric Functions Calculator
Calculate all six trigonometric functions
How to Use This Calculator
Enter the Angle
Input any angle value you want to calculate all trigonometric functions for.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad).
Calculate
Click "Calculate All Functions" to see all six trigonometric functions (sin, cos, tan, csc, sec, cot) at once.
Review Results
View all function values and verify relationships between them, such as the Pythagorean identity.
Formula
The Six Trigonometric Functions:
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
csc(θ) = 1 / sin(θ) = hypotenuse / opposite
sec(θ) = 1 / cos(θ) = hypotenuse / adjacent
cot(θ) = 1 / tan(θ) = adjacent / opposite
Key Relationships:
- tan(θ) = sin(θ) / cos(θ) (quotient identity)
- sin²(θ) + cos²(θ) = 1 (Pythagorean identity)
- Each reciprocal pair multiplies to 1: sin·csc = 1, cos·sec = 1, tan·cot = 1
About Trigonometric Functions Calculator
The Trigonometric Functions Calculator calculates all six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for any angle in degrees or radians. This comprehensive tool provides all trigonometric values in one place, making it perfect for students, engineers, and anyone working with trigonometry.
What are Trigonometric Functions?
Trigonometric functions relate angles in a right triangle to ratios of side lengths. There are six main functions: three primary (sin, cos, tan) and three reciprocal (csc, sec, cot). These functions are fundamental in mathematics, physics, engineering, and many other fields.
When to Use This Calculator
- Complete Analysis: Get all six trigonometric values for an angle at once
- Verification: Verify relationships between functions (e.g., Pythagorean identity)
- Problem Solving: Solve trigonometric equations and problems
- Learning: Understand how all trigonometric functions relate
- Quick Reference: Get all values without using separate calculators
Why Use Our Calculator?
- ✅ All Six Functions: Calculate sin, cos, tan, csc, sec, and cot simultaneously
- ✅ Visual Display: Color-coded results for easy identification
- ✅ Relationship Verification: Shows how functions relate to each other
- ✅ Multiple Units: Supports both degrees and radians
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works perfectly on all devices
- ✅ Educational: Helps understand trigonometric function relationships
Function Categories
- Primary Functions: sin, cos, tan - the most commonly used
- Reciprocal Functions: csc, sec, cot - inverses of the primary functions
- Co-functions: sin and cos are cofunctions, tan and cot are cofunctions, sec and csc are cofunctions
Frequently Asked Questions
What are the six trigonometric functions?
The six trigonometric functions are: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). The last three are reciprocals of the first three.
Why are some functions undefined for certain angles?
Functions become undefined when their denominators equal zero. For example, tan(90°) is undefined because cos(90°) = 0, and tan = sin/cos. Similarly, csc(0°) is undefined because sin(0°) = 0, and csc = 1/sin.
What's the relationship between all six functions?
The primary relationships are: (1) Reciprocal: sin·csc = 1, cos·sec = 1, tan·cot = 1, (2) Quotient: tan = sin/cos, cot = cos/sin, (3) Pythagorean: sin² + cos² = 1.
When would I need all six functions?
You might need all six when solving complex trigonometric equations, verifying identities, working with reciprocal relationships, or when specific problems require different function forms.
Can I calculate these functions manually?
For standard angles (30°, 45°, 60°, etc.), yes, using exact values. For other angles, you'd typically use a calculator or lookup tables. This calculator provides instant, accurate results for any angle.