tan2phi

tan2phi is a mathematical expression often encountered in trigonometry and physics, particularly when dealing with transformations or rotations. It represents the tangent of an angle that is twice another angle, commonly denoted as phi (φ). The formula for tan2phi is derived from the double angle identity for the tangent function, which states that tan(2θ) = (2tanθ) / (1 - tan²θ). Therefore, tan2phi can be written as (2tanφ) / (1 - tan²φ).

This expression is fundamental in areas such as the Mohr's circle of stress, where it relates the angle of rotation of coordinate axes to the orientation of principal stresses. In this context, tan2φ is used to find the angle of the principal planes. It also appears in the analysis of electrical circuits, particularly in the study of AC circuits and impedance, and in various mechanical engineering applications involving rotational dynamics. The value of tan2phi is undefined when 1 - tan²φ = 0, which occurs when tanφ = ±1, meaning φ = π/4 + nπ/2 for any integer n.