arctan
Represents the inverse tangent (arctangent) function in mathematical expressions, returning angles in radians.
Overview
Essential in trigonometry and mathematical analysis for finding angles when given a ratio of sides or coordinates. Common applications include:
- Converting Cartesian coordinates to polar form
- Solving geometric problems involving angles
- Computing phase angles in signal processing
- Frequently used in physics and engineering calculations where angular measurements are needed
Particularly valuable when working with right triangles or analyzing periodic phenomena, often appearing alongside other inverse trigonometric functions.
Examples
Finding the angle in a right triangle given the ratio of sides.
\theta = \arctan\left(\frac{y}{x}\right)Expressing the inverse tangent of a polynomial fraction.
f(x) = \arctan\left(\frac{2x+1}{x^2-1}\right)Computing the angle between two vectors using dot product.
\alpha = \arctan\left(\frac{\|\vec{a} \times \vec{b}\|}{\vec{a} \cdot \vec{b}}\right)