You’re used to seeing points in the xy-plane displayed in the (x, y) rectangular form. But when dealing with polar equations, you view these points in their polar form. To convert (x, y) from rectangular to polar form on the TI-83 Plus graphing calculator:
- Press [2nd][APPS] to access the Angle menu. (On the TI-83, press [2nd]MATRX].)
- Press [5] to select theoption.
- Enter the point (x, y) and press [ENTER] to display r in thepolar form of the point.To do so, enter the x-coordinate, press [.], enter the y-coordinate, press [ ) ], and then press [ENTER]. The value of r appears on the right of the screen.
- Press [2nd][APPS][6] to select theoption from the Angle menu. (On the TI-83, press [2nd][MATRX][6].)
- Enter the point (x, y) and press [ENTER] to displayin thepolar form of the point.will be in degrees if the calculator is in Degree mode, or it will be measured in radians if the calculator is in Radian mode.
Cartesian and Polar coordinate converting
In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes.
The calculator will convert the polar coordinates to rectangular (Cartesian) and vice versa, with steps shown.
Cartesian coordinates in the figure below: (2,3)
A Polar coordinate system is determined by a fixed point, a origin or pole, and a zero direction or axis. Each point is determined by an angle and a distance relative to the zero axis and the origin.
Polar coordinates in the figure above: (3.6, 56.31)
Polar coordinates can be calculated from Cartesian coordinates like
r = (x2 + y2)1/2 (1)
where
r = distance from origin to the point
x = Cartesian x-coordinate
y = Cartesian y-coordinate
θ = atan(y / x)
= tan-1(y / x) (2)
where
θ = angle relative to the zero axis (degrees)
Cartesian coordinates can be calculated from Polar coordinates like
x = r cos(θ) (3)
y = r sin(θ) (4)
Online Cartesian to Polar Coordinates Converter
Online Polar to Cartesian Coordinates Converter
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