📐 Trigonometry Calculator
Calculate sine, cosine, tangent, and other trigonometric functions for any angle. Get instant results in both degrees and radians with high precision.
What is a Trigonometry Calculator?
A trigonometry calculator is an essential mathematical tool that computes the values of trigonometric functions for any given angle. These functions - sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) - form the foundation of trigonometry and are crucial in various fields including physics, engineering, astronomy, and computer graphics.
Our calculator accepts angles in both degrees and radians, making it versatile for different mathematical contexts. Whether you're a student working on homework, an engineer designing structures, or a programmer implementing graphics algorithms, this tool provides accurate trigonometric values instantly.
The calculator uses high-precision algorithms to ensure accurate results up to 6 decimal places. It handles special cases like undefined values for certain angles (such as tan(90°)) and provides clear error messages when appropriate. This makes it reliable for both educational purposes and professional applications.
Calculate Trigonometric Functions
How to Use the Trigonometry Calculator
- Enter Your Angle: Type the angle value in the input field. You can enter any real number, including negative angles and angles greater than 360°.
- Select the Unit: Choose whether your angle is in degrees or radians. Degrees are more common in geometry and everyday applications, while radians are preferred in calculus and advanced mathematics.
- Click Calculate: Press the "Calculate All Functions" button to compute all six trigonometric functions simultaneously.
- Review Results: The calculator displays all trigonometric values with high precision. It also shows the angle conversion between degrees and radians.
- Special Cases: For angles where certain functions are undefined (like tan(90°)), the calculator will display "Undefined" with an explanation.
The calculator handles all quadrants correctly, so you can input angles like 120°, 225°, or -45° and get accurate results. It also works with decimal values, so you can calculate functions for angles like 37.5° or 1.234 radians.
Common Angle Values Reference
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | Undefined |
Benefits of Using Our Calculator
🎯 High Precision
Get results accurate to 6 decimal places, suitable for scientific and engineering applications.
⚡ Instant Results
No waiting or page reloads. Server-side calculations provide immediate, reliable results.
📊 All Functions
Calculate all six trigonometric functions simultaneously - sin, cos, tan, cot, sec, and csc.
🔄 Unit Conversion
Automatic conversion between degrees and radians helps you work in your preferred unit system.
📱 Mobile Ready
Fully responsive design works perfectly on phones, tablets, and desktop computers.
🆓 Always Free
No registration, no fees, no limitations. Professional-grade calculations at no cost.
Frequently Asked Questions
What are trigonometric functions used for?
Trigonometric functions are fundamental in mathematics and have countless real-world applications. They're used in physics to analyze waves and oscillations, in engineering for structural design and signal processing, in computer graphics for 3D rendering and animations, and in navigation for calculating distances and directions. Musicians use them to understand sound waves, architects use them for building design, and astronomers use them to calculate celestial positions.
What's the difference between degrees and radians?
Degrees and radians are two different units for measuring angles. Degrees divide a circle into 360 equal parts, making them intuitive for everyday use. Radians measure angles based on the radius of a circle - one radian is the angle created when the arc length equals the radius. There are 2π radians in a full circle (approximately 6.28318). While degrees are more common in geometry and everyday applications, radians are preferred in calculus and physics because they simplify many mathematical formulas.
Why are some values listed as "Undefined"?
Certain trigonometric functions become undefined at specific angles because they involve division by zero. For example, tan(90°) is undefined because tan = sin/cos, and cos(90°) = 0. Similarly, cot(0°) is undefined because cot = cos/sin, and sin(0°) = 0. These undefined points are called discontinuities or asymptotes in the function graphs. Understanding where functions are undefined is crucial for solving equations and analyzing mathematical models.
How accurate is this calculator?
Our calculator provides results accurate to 6 decimal places, which exceeds the precision needed for most practical applications. The calculations use PHP's built-in mathematical functions, which implement IEEE 754 double-precision floating-point arithmetic. This level of accuracy is sufficient for engineering calculations, scientific research, and educational purposes. For specialized applications requiring extreme precision, dedicated mathematical software may be more appropriate.
Can I use negative angles or angles greater than 360°?
Yes! Our calculator handles any real number as an angle input. Negative angles represent clockwise rotation from the positive x-axis, while positive angles represent counterclockwise rotation. Angles greater than 360° simply represent multiple rotations plus an additional angle. The calculator automatically normalizes these values using the periodic nature of trigonometric functions. For example, sin(370°) = sin(10°) because 370° = 360° + 10°.