Trigonometry Calculator
Result:
sin(30°) = 0.5000
cos(30°) = 0.8660
tan(30°) = 0.5774
csc(30°) = 2.0000
sec(30°) = 1.1547
cot(30°) = 1.7321
What is a Trigonometry Calculator?
A trigonometry calculator is a comprehensive mathematical tool that computes trigonometric functions (sin, cos, tan) and their inverses, solves triangles using the law of cosines and sines, and provides unit circle coordinates. It handles both degrees and radians, making it essential for geometry, physics, engineering, and advanced mathematics.
Trigonometry studies the relationships between angles and sides in triangles, with applications in navigation, architecture, astronomy, and wave analysis. Our calculator provides accurate computations for all six trigonometric functions and their reciprocals, supporting both theoretical study and practical problem-solving.
How It Works
Select Function
Choose trigonometric operation
Input Values
Enter angles or sides
Get Results
View calculated values
Common Examples
Special Angles (30°)
sin(30°) = 0.5000
cos(30°) = 0.8660
tan(30°) = 0.5774
Unit Circle: (√3/2, 1/2)
Special Angles (45°)
sin(45°) = 0.7071
cos(45°) = 0.7071
tan(45°) = 1.0000
Unit Circle: (√2/2, √2/2)
Special Angles (60°)
sin(60°) = 0.8660
cos(60°) = 0.5000
tan(60°) = 1.7321
Unit Circle: (1/2, √3/2)
Right Triangle (3-4-5)
Angles: 36.87°, 53.13°, 90°
sin(36.87°) = 0.6000
cos(36.87°) = 0.8000
tan(36.87°) = 0.7500
Calculation Table
| Function | Definition | Range | Period |
|---|---|---|---|
| sin(θ) | opposite / hypotenuse | [-1, 1] | 2π |
| cos(θ) | adjacent / hypotenuse | [-1, 1] | 2π |
| tan(θ) | opposite / adjacent | (-∞, ∞) | π |
| csc(θ) | 1 / sin(θ) | (-∞, -1] ∪ [1, ∞) | 2π |
| sec(θ) | 1 / cos(θ) | (-∞, -1] ∪ [1, ∞) | 2π |
| cot(θ) | 1 / tan(θ) | (-∞, ∞) | π |
Frequently Asked Questions
What are the six trigonometric functions?
The six functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). The first three are primary, while the last three are their reciprocals.
What's the difference between degrees and radians?
Degrees divide a circle into 360 parts, while radians use the circle's radius. 180° = π radians. Radians are preferred in calculus and advanced mathematics.
How do I remember the unit circle values?
Use the pattern for special angles: 0°, 30°, 45°, 60°, 90°. For sine: 0, 1/2, √2/2, √3/2, 1. For cosine: reverse the sine values.
What are inverse trigonometric functions?
Inverse functions (arcsin, arccos, arctan) find the angle when given the ratio. For example, if sin(θ) = 0.5, then arcsin(0.5) = 30°.
How accurate are the calculations?
Our calculator uses JavaScript's built-in Math functions with double-precision floating-point arithmetic, providing accuracy to about 15-17 decimal places.
Is this calculator free to use?
Yes, this trigonometry calculator is completely free with no registration required. Perfect for students, engineers, and anyone studying mathematics or physics.