tan
Represents the trigonometric tangent function, calculated as the ratio of sine to cosine.
Overview
Essential in trigonometry and mathematical analysis for describing relationships between angles and ratios in right triangles and periodic functions.
- Fundamental in calculus for analyzing periodic behavior and wave functions
- Widely used in physics for modeling oscillations and waves
- Critical in engineering for structural analysis and signal processing
- Often appears alongside sine and cosine in mathematical expressions
- Particularly important in geometry for calculating slopes and angles
Examples
Calculating the tangent of an angle in a right triangle.
\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b}Trigonometric identity relating tangent to sine and cosine.
\tan x = \frac{\sin x}{\cos x}Double angle formula for tangent.
\tan 2x = \frac{2\tan x}{1-\tan^2 x}