Concept:
Polar coordinates (r, θ) are another way to specify locations in the plane. They are related to rectangular coordinates (x, y) by the formulas
x = r cos θ, y = r sin θ
and
r2 = x2 + y2, tan θ = y/x
Polar Coordinates
Rectangular coordinates (x, y)
(
,
)
Polar coordinates (r, θ)
(
,
o)
INSTRUCTIONS
Enter the coordinates for a point in either the rectangular coordinate system or the polar coordinate system, and click the corresponding button. The coordinates of the point will be converted to the other form and the point will be displayed in the new coordinate system.
The coordinates of a point in either form may be entered by typing the values in the boxes, by using the sliders, or by clicking on the point in the coordinate grid
When typing point coordinates, be sure that x-, y-, and r-values are between –10 and 10 so that they remain on the grid. Values for θ are measured in degrees and can have any value.
If the graph area gets cluttered, click on the “Clear the grid” button to erase all points.
EXPLORATIONS
Exploration 1:
Plot several points in polar coordinates that all have the same value of r. Can you make a general statement about sets of points in polar coordinates for which r = a constant?
Exploration 2:
Plot several points in polar coordinates that all have the same value of θ. Can you make a general statement about sets of points in polar coordinates for which θ = a constant?
Exploration 3:
Plot the points (5, 72°), (5, 432°), (5, –288°), (–5, 252°), and (–5, –108°). What can be said about these points? Can you generalize the result?
