arctan and the gradient

Remark — The role of arctan in coordinate geometry

The gradient of a line $y=mx+q$ is related to its angle of inclination $\theta$ with the $x$-axis by the relation $m = \tan\theta$, whence $\theta = \arctan m$. It is thanks to this relation that we can speak of the “angle between two lines” starting from their gradients.

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Topics: Trigonometry
Concepts: Arctangent · Gradient · Line
Functions: Arctangent · Inverse trigonometric functions
Skills: Analytic geometry