Polar coordinate system
A polar coordinate system consists of a fixed point O and a half line (axis) starting from this point - do my homework for me . Any point P of the plane can then be uniquely defined by specifying its polar coordinates r and ϕ.
A polar coordinate system consists of a fixed point O, the pole (starting point), as well as a half line starting from this point, the polar axis as zero direction - do my algebra homework . On this axis (as on the number line), corresponding lengths can be plotted or measured.
Any point P of the plane can then be unambiguously defined by specifying the following coordinates:
- the (positive) distance r of the point P from the pole;
- the angle ϕ by which the number ray must be rotated in the mathematically positive sense, so that it passes through P.
(This angle ϕ is also called phase, amplitude, or anomaly).
For the polar coordinates r and ϕ holds:
0≤r∞ 0°≤ϕ360°(resp.0≤ϕ2π).
Relationship between polar coordinates and cartesian coordinates
Choosing the coordinate origin of a Cartesian coordinate system as the pole and the positive x-axis as the polar axis (of a polar coordinate system), the following relationships can be derived:
x=r⋅cosϕ y=r⋅sinϕ
resp.
r=√(x2+y2)
cosϕ=x/√(x^2+y^2); sinϕ=y/√(x^2+y^2) (resp. ϕ=arc tan(y/x)).
Note: For x=y=0 the angle ϕ is not defined, for x=0 , y≠0 ϕ=±π/2.
With the help of the above equations - pay someone to do your math homework , polar coordinates can be converted into Cartesian coordinates (and vice versa). One speaks then of a so-called coordinate transformation.
See also:
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