Guides, worked examples and explainers about the inverse tangent, atan2, slopes, angles and trigonometry.
Learn what arctan means, how it undoes the tangent, why its answers lie between −90° and 90°, and how to use it with worked examples.
Read article: What is the inverse tangent (arctan)? A clear guide with examplesPlain arctan cannot tell opposite quadrants apart. See how atan2(y, x) returns the full angle from −180° to 180°, with a quadrant table and examples.
Read article: atan vs atan2: why the two-argument arctangent mattersA step-by-step method for finding a right-triangle angle with arctan, plus how to get the hypotenuse and the other angle, with three worked examples.
Read article: How to find an angle from the opposite and adjacent sidesThe exact inverse tangent values for 0, 1/√3, 1, √3 and more, how they come from the 30-60-90 and 45-45-90 triangles, and a full reference table.
Read article: Exact values of arctan: the special angles to know by heartWhy d/dx arctan x = 1/(1 + x²), how to integrate arctan x by parts, the Taylor series, and how these results lead to the Leibniz formula for π.
Read article: Derivative and integral of arctan, with proofsFrom road grades and roof pitch to robot navigation, GPS bearings and audio phase, here is where the inverse tangent is used every day, with numbers.
Read article: Arctan in real life: 7 places the inverse tangent does the work
