Trigonometry Calculator
Calculate trigonometric functions (sin, cos, tan) and their inverses with degrees and radians. Perfect for math, physics, engineering, and navigation calculations.
Trigonometric Functions Calculator
Common Trigonometry Examples
Click on these links to see instant calculations with common angles:
Trigonometric Functions
Trigonometry deals with the relationships between angles and sides in triangles. The basic trigonometric functions are sine, cosine, and tangent, which relate angles to ratios of triangle sides.
Basic Trigonometric Ratios
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent = sin(θ) / cos(θ)
Angle conversion: radians = degrees × (π/180)
degrees = radians × (180/π)
Common Trigonometric Values
| Angle (Degrees) | Angle (Radians) | sin(θ) | cos(θ) | tan(θ) |
|---|---|---|---|---|
| 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 |
- Mathematics: Solve triangle problems and trigonometric equations
- Physics: Analyze wave motion, oscillations, and periodic phenomena
- Engineering: Design structures, analyze forces, and signal processing
- Navigation: Calculate distances, bearings, and GPS coordinates
- Computer Graphics: Rotate objects, create animations, and 3D transformations
Frequently Asked Questions
What are the basic trigonometric functions?
The basic trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles of a triangle to the ratios of its sides. Sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
What is the difference between degrees and radians?
Degrees and radians are two units for measuring angles. A full circle is 360 degrees or 2π radians. To convert: degrees = radians × (180/π), radians = degrees × (π/180). Radians are often used in calculus and advanced mathematics.
What are inverse trigonometric functions?
Inverse trigonometric functions (arcsin, arccos, arctan) find the angle when given the ratio. For example, if sin(θ) = 0.5, then arcsin(0.5) = θ = 30° or π/6 radians. They're the reverse of regular trig functions.