Trigonometry Calculator
Type an angle and instantly see the sin / cos / tan answer — exact values alongside decimals, tools tucked away
Angle Input
📋 Special Angles Table (16 standard angles)▶
| Angle | sin | cos | tan |
|---|
cos values run in reverse.
tan = sin ÷ cos.
⭕ Unit Circle Visualization▶
↺ Inverse Trig Calculator▶
⇄ DMS Converter▶
➡️ Done? Here is what you might need next
✓ Trig Identity Verification▶
🔁 Angle Conversion▶
📈 Trig Function Graph
About This Trigonometry Calculator
This calculator provides complete trigonometric function computation, including the basic functions (sin, cos, tan) and their reciprocals (csc, sec, cot), with degree/radian conversion, special angle lookup, unit circle visualization and identity verification. Suitable for high school and college students as well as engineers.
How To Use
- Enter an angle value and select the unit (degree or radian)
- Choose a trig function to focus, or view all function results
- View results including exact values and decimals
- Use the unit circle visualization to understand the geometric meaning
- Verify trigonometric identities to deepen understanding
- Use the quick-select buttons to look up special angle values
- Observe sine, cosine, tangent waveforms through the function graph
Calculator Features
- Complete trig functions: sin, cos, tan, csc, sec, cot
- Inverse functions: arcsin, arccos, arctan
- Angle conversion: degrees ↔ radians, DMS ↔ decimal degrees
- Special angles table: 0°, 30°, 45°, 60°, 90° with memory aids
- Unit circle visualization: intuitive geometric understanding
- Identity verification: instantly checks sin²θ + cos²θ = 1, etc.
- Function graph: sine, cosine, tangent waveform visualization
- Real-time calculation: instant results as you type
- High precision with exact values covering all four quadrants
- Bilingual support: full Traditional Chinese and English
Why Use This Calculator
- Student learning: essential for high school and college math
- Homework check: quickly verify trig problem answers
- Engineering: a common trig tool for calculations
- Visual learning: understand abstract concepts through graphics
- Anytime: an online tool, no download or install needed
Frequently Asked Questions
How do I memorize special-angle trig values?
Memory trick: sin values from small to large are √0/2, √1/2, √2/2, √3/2, √4/2 (i.e. 0, 1/2, √2/2, √3/2, 1), matching 0°, 30°, 45°, 60°, 90°. cos runs in reverse, large to small. tan = sin ÷ cos.
How do degrees and radians convert?
Formula: radians = degrees × π/180, degrees = radians × 180/π. E.g. 180° = π rad, 90° = π/2 rad, 1 rad ≈ 57.2958°. The key fact: π radians = 180 degrees.
Why is tan(90°) undefined?
Because tan(90°) = sin(90°)/cos(90°) = 1/0, and division by zero is undefined. On the unit circle, at 90° the x-coordinate (cos) is 0, so the y/x ratio cannot be computed. Similarly cot(0°), cot(180°) are also undefined.
What are trigonometric identities?
Trigonometric identities are equations true for all angles. The most basic is the Pythagorean identity sin²θ + cos²θ = 1, derived from the Pythagorean theorem. Others include 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ.
How does the unit circle help understand trig functions?
In the unit circle, the center is at the origin with radius 1. Rotating counterclockwise from the positive x-axis by angle θ to a point on the circle, the x-coordinate is cos(θ) and the y-coordinate is sin(θ). This geometric view makes trig definitions intuitive.
How are negative angles calculated?
Negative angles mean clockwise rotation. sin(-θ) = -sin(θ), cos(-θ) = cos(θ), tan(-θ) = -tan(θ). For example sin(-30°) = -sin(30°) = -1/2.
How are angles greater than 360° handled?
Trig functions are periodic; sin and cos have a period of 360° (2π). Angles above 360° are normalized automatically. E.g. sin(390°) = sin(390° - 360°) = sin(30°) = 1/2.
Applications of Trigonometry
- Physics: force components, waves, simple harmonic motion
- Engineering: structural analysis, circuits, signal processing
- Surveying: measuring height, distance and angles
- Astronomy: celestial positions, orbital parameters
- Computer graphics: 3D rotation, animation, game development
- Music: sound wave analysis, audio synthesis
Usage Tips
- Use quick-select buttons to instantly view common special angles
- Results auto-update when switching degree/radian mode
- Identity verification helps understand relationships between functions
- View the unit circle to intuitively understand sin and cos geometry
- The function graph shows periodicity, aiding understanding
- Use keyboard shortcuts (Ctrl+R/S/P, D/R) to work faster
