arctg
Represents the inverse tangent (arctangent) function in mathematical expressions, returning angles in radians.
Overview
Serves as a fundamental inverse trigonometric function essential in mathematics and applied sciences, particularly when determining angles from ratios.
- Common in coordinate transformations and navigation calculations
- Used extensively in physics for analyzing periodic motion and waves
- Appears frequently in engineering applications, especially in control systems and signal processing
- Alternative to the more commonly used \arctan notation, particularly in European mathematical texts
Examples
Finding the angle in a right triangle given the ratio of sides.
\theta = \arctg\left(\frac{a}{b}\right)Expressing the solution to a trigonometric equation.
x = \arctg(2) + \pi n,\quad n \in \mathbb{Z}Calculating the angle of intersection between two lines.
\alpha = \arctg\left(\left|\frac{m_1 - m_2}{1 + m_1m_2}\right|\right)