Sistem koordinat polar: Perbedaan antara revisi

Adding any number of full [[turn (geometry)|turn]]s (360°) to the angular coordinate does not change the corresponding direction. Also, a negative radial coordinate is best interpreted as the corresponding positive distance measured in the opposite direction. Therefore, the same point can be expressed with an infinite number of different polar coordinates {{nowrap|(''r'', ''φ'' ± ''n''×360°)}} or {{nowrap|(−''r'', ''φ'' ± (2''n'' + 1)180°)}}, where ''n'' is any [[integer]].<ref>{{Cite web| url = http://www.fortbendisd.com/campuses/documents/Teacher/2006%5Cteacher_20060413_0948.pdf| title = Polar Coordinates and Graphing| accessdate = 2006-09-22| date = 2006-04-13| format = PDF}}</ref> Moreover, the pole itself can be expressed as (0,&nbsp;''φ'') for any angle ''φ''.<ref>{{Cite book|title=Precalculus: With Unit-Circle Trigonometry|last=Lee|first=Theodore|author2=David Cohen |author3=David Sklar |year=2005|publisher=Thomson Brooks/Cole|edition=Fourth|isbn=0-534-40230-5}}</ref>▼

Where a unique representation is needed for any point, it is usual to limit ''r'' to [[non-negative number]]s ({{nowrap|''r'' ≥ 0}}) and ''φ'' to the [[interval (mathematics)|interval]] [0,&nbsp;360°) or (−180°,&nbsp;180°] (in radians, [0,&nbsp;2π) or (−π,&nbsp;π]).<ref>{{Cite book|title=Complex Analysis (the Hitchhiker's Guide to the Plane)|first=Ian|last=Stewart|author2=David Tall|year=1983|publisher=Cambridge University Press|isbn=0-521-28763-4}}</ref> One must also choose a unique azimuth for the pole, e.g., ''φ''&nbsp;=&nbsp;0.▼