Angle of Tangent to Radius in Polar Coordinates
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This theorem requires a proof..
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Theorem
Let $C$ be a curve embedded in a plane defined by polar coordinates.
Let $P$ be the point at $\left\langle{r, \theta}\right\rangle$.
Then the angle $\psi$ made by the tangent to $C$ at $P$ with the radial coordinate is given by:
- $\tan \psi = r \dfrac {\mathrm d \theta} {\mathrm d r}$
Proof
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Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 1.3$: Families of Curves. Orthogonal Trajectories
