Trigonometry Calculator
Comprehensive trigonometry calculations and visualizations.
Visualization
Trigonometry Formulas
Right Triangle
- Pythagorean Theorem: \[ a^2 + b^2 = c^2 \]
- \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
- \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
- \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Oblique Triangle
- Law of Sines: \[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \]
- Law of Cosines: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]
- Area: \[ \text{Area} = \frac{1}{2}ab\sin(C) \]
Unit Circle
- \[ \sin(\theta) = y \]
- \[ \cos(\theta) = x \]
- \[ \tan(\theta) = \frac{y}{x} \]
- \[ x^2 + y^2 = 1 \]
Common Values
- \[ \sin(30°) = \frac{1}{2}, \cos(30°) = \frac{\sqrt{3}}{2} \]
- \[ \sin(45°) = \frac{1}{\sqrt{2}}, \cos(45°) = \frac{1}{\sqrt{2}} \]
- \[ \sin(60°) = \frac{\sqrt{3}}{2}, \cos(60°) = \frac{1}{2} \]
Applications
- Navigation and surveying
- Architecture and construction
- Physics and engineering
- Computer graphics
- Music and sound analysis