Tangential Angle

Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken (Herausgeber)

Buch | Softcover

224 Seiten

2010
Betascript Publishing (Verlag)
978-613-1-15684-7 (ISBN)

Infos

High Quality Content by WIKIPEDIA articles! In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the x-axis. (Note, some authors define the angle as the deviation from the direction of the curve at some fixed starting point. This is equivalent to the definition given here by the addition of a constant to the angle or by rotating the curve). If a curve is given parametrically by (x(t), y(t)) then the tangential angle varphi at t is defined (up to a multiple of 2 ) by frac{(x'(t), y'(t))}{ x'(t), y'(t) } = (cos varphi, sin varphi). Thus the tangential angle specifies the direction of the velocity vector (x'(t), y'(t)) while the speed specifies its magnitude. The vector frac{(x'(t), y'(t))}{ x'(t), y'(t) } is called the unit tangent vector, so an equivalent definition is that the tangential angle at t is the angle varphi such that (cos varphi, sin varphi) is the unit tangent vector at t. If the curve is parameterized by arc length s, so x'(s), y'(s) = 1, then the definition simplifies to (x'(s), y'(s)) = (cos varphi, sin varphi).

Produkt-Details

• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 613-1-15684-0 / 6131156840
• ISBN-13: 978-613-1-15684-7 / 9786131156847
• Zustand: Neuware