Inverse Tangent Calculator

The inverse tangent function is the inverse of the standard trigonometric tangent function. If you have an angle theta ($ heta$) whose tangent is equal to a number $x$, expressed mathematically as $ an( heta) = x$, then the inverse tangent returns that angle: $ heta = an^{-1}(x)$ or $ heta = ext{arctan}(x)$. The standard range of output for arctan is strictly bounded between $-rac{\pi}{2}$ and $rac{\pi}{2}$ radians, or $-90^ ext{o}$ and $90^ ext{o}$, aligning with the first and fourth quadrants of the Cartesian coordinate system.

Imagine you need to find the angle of elevation for a ramp that rises 5 meters vertically for every 5 meters of horizontal run. First, you calculate the ratio of the opposite side to the adjacent side, which is $5 / 5 = 1$. Next, you apply the inverse tangent function to that ratio: $ heta = ext{arctan}(1)$. Because the tangent of $45^ ext{o}$ equals $1$, the calculator evaluates this input and outputs an angle of $45^ ext{o}$ (or $rac{\pi}{4}$ radians). This tells you the ramp slopes upward at exactly a $45$-degree angle.

Always verify whether your final calculation requires degrees or radians before applying the output to engineering or physics formulas. Keep in mind that standard arctan functions have restricted output ranges; if you are working with full 360-degree coordinates (x and y), consider using a two-argument atan2 function instead to avoid directional ambiguity. Double-check that your input value represents a proper ratio of sides rather than a direct length dimension.