Polar Coordinates

We have the following relationships between polar coordinates and rectangular coordinates:

Ex 1 Find a set of polar coordinates for the point with rectangular coordinates .

Sol , so we can take . Since , we can take . Therefore is a set of polar coordinates for this point.

Ex 2 Find rectangular coordinates for the point which has polar coordinates .

Sol and , so the point has rectangular coordinates .

Pr A Find a polar equation for the circle with rectangular equation .

Pr B Find the standard form of the rectangular equation of the circle with polar equation .

Pr C Find two sets of polar coordinates for the point with rectangular coordinates .

Pr 1 Find a set of polar coordinates for the point with rectangular coordinates .

Pr 2 Find a set of polar coordinates for the point with rectangular coordinates .

Pr 3 Find rectangular coordinates for the point which has polar coordinates .

Pr 4 Find a polar equation for the line with equation in rectangular coordinates.

Pr 5 Find a polar equation for the line with equation in rectangular coordinates.

Pr 6 Find a polar equation for the circle with equation in rectangular coordinates.

Pr 7 Find a rectangular equation for the cardioid with polar equation .

Pr 8 Find the points of intersection of the curves with polar equations and .