Trigonometry Calculator
Calculate angles, sides, trigonometric functions, and solve triangles with this comprehensive trigonometry calculator. Get step-by-step solutions for right triangles and general trigonometry problems.
Results
Right Triangle Solution
| Element | Value |
|---|---|
| Side a (opposite ∠α) | - |
| Side b (opposite ∠β) | - |
| Hypotenuse c | - |
| Angle α | - |
| Angle β | - |
| Area | - |
| Perimeter | - |
Trigonometric Function Results
Function: sin(30°) = 0.5
Other related functions:
| Function | Value |
|---|---|
| sin(θ) | - |
| cos(θ) | - |
| tan(θ) | - |
| csc(θ) | - |
| sec(θ) | - |
| cot(θ) | - |
Unit Circle Results
Angle: 45°
Coordinates: (0.7071, 0.7071)
Trigonometric values:
| Function | Value |
|---|---|
| sin(θ) | 0.7071 |
| cos(θ) | 0.7071 |
| tan(θ) | 1 |
About Trigonometry
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The word trigonometry comes from the Greek words "trigonon" (triangle) and "metron" (measure).
Key Concepts
Trigonometry provides powerful tools to solve geometric problems involving triangles:
Right Triangles
A right triangle has one angle equal to 90° (π/2 radians). The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The Pythagorean theorem relates the sides:
a² + b² = c² (where c is the hypotenuse)
The trigonometric functions relate the angles to the ratios of the sides:
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
Trigonometric Functions
The six main trigonometric functions are:
- Sine (sin)
- Cosine (cos)
- Tangent (tan)
- Cosecant (csc) = 1/sin
- Secant (sec) = 1/cos
- Cotangent (cot) = 1/tan
Unit Circle
The unit circle is a circle with radius 1 centered at the origin (0,0) in the coordinate plane. It provides a geometric interpretation of trigonometric functions:
- For any angle θ, the x-coordinate is cos(θ)
- The y-coordinate is sin(θ)
- The slope of the line connecting the origin to the point is tan(θ)
Applications
Trigonometry has wide applications in mathematics, physics, engineering, and many other fields:
- Navigation and GPS systems
- Architecture and construction
- Astronomy and celestial navigation
- Physics (waves, oscillations, circular motion)
- Computer graphics and game development
- Surveying and geography
- Electrical engineering (signal processing)