for whatever point (x, y):
r= sqrt( x2+ y2 ) from pythagorean theorem.
basic trig function since the x and y axes are perpendicular to each other:
tan theta = y/x (opposite over adjacent)
theta = tan-1 (y/x)
(r, theta) ----> ( sqrt( x2+ y2 ), tan-1 (y/x) )
You do not have to. You could use polar coordinates, if you prefer.
The abscissa in Cartesian coordinates. In polar coordinates, it would be the radius .or domain
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x2+y2=2y into polar coordinates When converting Cartesian coordinates to polar coordinates, three standard converstion factors must be memorized: r2=x2+y2 r*cos(theta)=x r*sin(theta)=y From these conversions, you can easily get the above Cartesian equation into polar coordinates: r2=2rsin(theta), which reduces down (by dividing out 1 r on both sides) to: r=2sin(theta)
If cartesian coordinates are used then the second number in an ordered pair is the y coordinate, also known as the ordinate. If polar coordinates are used then the second number is the angle.
Some problems are easier to solve using polar coordinates, others using Cartesian coordinates.
The point whose Cartesian coordinates are (2, 0) has the polar coordinates R = 2, Θ = 0 .
You do not have to. You could use polar coordinates, if you prefer.
The point whose Cartesian coordinates are (-3, -3) has the polar coordinates R = 3 sqrt(2), Θ = -0.75pi.
The abscissa in Cartesian coordinates. In polar coordinates, it would be the radius .or domain
the equation that convert from cartesian to polar coordinates and vice versa r = sqrt (x*x+y*y); phi = atan2 (y, x); x = r*cos (phi); y = r*sin (phi);
The spherical to cartesian unit vectors are used to convert coordinates between spherical and cartesian systems. They are denoted as ( hatr ), ( hattheta ), and ( hatphi ), representing the radial, azimuthal, and polar directions respectively.
Polar Co-ordinates are non-Cartesian co-ordinates. Since most of the Graphics Package do not support non-Cartesian co-ordinates,Polar co-ordinates should be converted to Cartesian form.
53
x2+y2=2y into polar coordinates When converting Cartesian coordinates to polar coordinates, three standard converstion factors must be memorized: r2=x2+y2 r*cos(theta)=x r*sin(theta)=y From these conversions, you can easily get the above Cartesian equation into polar coordinates: r2=2rsin(theta), which reduces down (by dividing out 1 r on both sides) to: r=2sin(theta)
If the polar coordinates of a complex number are (r,a) where r is the distance from the origin and a the angle made with the x axis, then the cartesian coordinates of the point are: x = r*cos(a) and y = r*sin(a)
If cartesian coordinates are used then the second number in an ordered pair is the y coordinate, also known as the ordinate. If polar coordinates are used then the second number is the angle.