Trigonometry Calculator
Comprehensive trigonometry calculator for all your trigonometric needs
Common Trigonometric Values
0°
sin: 0
cos: 1
tan: 0
30°
sin: 1/2
cos: √3/2
tan: √3/3
45°
sin: √2/2
cos: √2/2
tan: 1
60°
sin: √3/2
cos: 1/2
tan: √3
90°
sin: 1
cos: 0
tan: ∞
120°
sin: √3/2
cos: -1/2
tan: -√3
135°
sin: √2/2
cos: -√2/2
tan: -1
150°
sin: 1/2
cos: -√3/2
tan: -√3/3
How to Use This Calculator
Enter the Angle
Input the angle value you want to perform trigonometric calculations for. You can enter any angle in degrees or radians.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad). The calculator will automatically convert between them.
Choose Display
Select whether you want to see all trigonometric functions, or focus on just sine, cosine, or tangent.
Calculate
Click "Calculate Trigonometry" to see all the trigonometric function values and verify key relationships.
Formula
Fundamental Trigonometric Functions:
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
Reciprocal Functions:
csc(θ) = 1 / sin(θ)
sec(θ) = 1 / cos(θ)
cot(θ) = 1 / tan(θ)
Key Identities:
sin²(θ) + cos²(θ) = 1 (Pythagorean Identity)
tan(θ) = sin(θ) / cos(θ) (Quotient Identity)
1 + tan²(θ) = sec²(θ)
1 + cot²(θ) = csc²(θ)
Unit Circle Definition:
On the unit circle: sin(θ) = y-coordinate, cos(θ) = x-coordinate
About Trigonometry Calculator
The Trigonometry Calculator is a comprehensive tool for all your trigonometric calculations. This calculator computes all six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for any angle, helping you solve trigonometry problems quickly and accurately.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between angles and sides of triangles, particularly right triangles. The word "trigonometry" comes from Greek words meaning "triangle" and "measure." Trigonometric functions describe these relationships and are fundamental to mathematics, physics, engineering, and many other fields.
When to Use This Calculator
- Homework Help: Solve trigonometry problems and verify your answers
- Right Triangle Problems: Find missing sides or angles in right triangles
- Wave Analysis: Calculate values for sine and cosine waves
- Physics Problems: Solve problems involving forces, vectors, and periodic motion
- Engineering: Design and analyze mechanical systems, structures, and circuits
- Navigation: Calculate distances, bearings, and positions
- Verification: Check manual calculations and verify trigonometric identities
Why Use Our Calculator?
- ✅ Complete Calculations: Get all six trigonometric functions at once
- ✅ Flexible Display: View all functions or focus on specific ones
- ✅ Multiple Units: Supports both degrees and radians
- ✅ Identity Verification: Automatically verifies key trigonometric relationships
- ✅ Educational: Shows relationships between functions
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works perfectly on all devices
- ✅ Accurate: High-precision calculations
Applications of Trigonometry
- Architecture: Calculate roof pitches, structural angles, and building dimensions
- Astronomy: Measure distances to stars and planets
- Music: Analyze sound waves and frequencies
- Computer Graphics: Rotate and transform objects
- GPS Navigation: Calculate positions and distances
- Physics: Analyze waves, oscillations, and periodic phenomena
Frequently Asked Questions
What are the most important trigonometric functions?
The three primary functions are sine (sin), cosine (cos), and tangent (tan). These are the most commonly used. The reciprocal functions (csc, sec, cot) are derived from these.
How do I memorize trigonometric values?
Start with the special angles: 0°, 30°, 45°, 60°, 90°. For these angles, memorize: sin(30°)=1/2, sin(45°)=√2/2, sin(60°)=√3/2. Use the unit circle to derive others. Practice regularly!
What's the difference between degrees and radians?
Degrees divide a circle into 360 parts, while radians divide it into 2π parts. 180° = π radians. Radians are often preferred in higher mathematics because they simplify many formulas.
When is tangent undefined?
Tangent is undefined when cos(θ) = 0, which occurs at 90°, 270°, and their multiples. At these angles, we're dividing by zero (tan = sin/cos).
How is trigonometry used in real life?
Trigonometry is used in architecture (calculating roof angles), engineering (designing structures), navigation (GPS and compass bearings), music (sound wave analysis), physics (wave mechanics), and computer graphics (rotations).
What is the unit circle and why is it important?
The unit circle is a circle with radius 1 centered at the origin. It's fundamental because: (1) cos(θ) = x-coordinate, sin(θ) = y-coordinate, (2) it extends trig functions beyond 90°, and (3) it shows periodic behavior and relationships between functions.