Converting Polar Coordinates to Cartesian
The polar coordinates are defined in terms of and , where is the distance of the point from the origin and is the angle made with the positive -axis.
Clearly, using trigonometry, if the Cartesian coordinates are then
If is the distance of a point from the origin and is the angle made with the positive -axis, then what will be the Cartesian coordinates of the point?
The Cartesian coordinates can be obtained from the distance of the point from the origin and the angle made with the positive -axis. Using trigonometry, we have
Thus, the Cartesian coordinates of the point are
Write the Cartesian coordinates as polar coordinates.
Let denote the distance between the origin and the point then
Now, let denote the angle made with the positive -axis, then we have
which both imply
Thus from and the polar coordinates of the Cartesian coordinates are
What are the Cartesian coordinates of the point whose distance from origin is and the angle made with the positive -axis is
Since the distance of the point from the origin is and the angle made with the positive -axis is the Cartesian coordinates are
Thus, the answer is
Write the Cartesian coordinates as polar coordinates.
Let denote the distance between the origin and the point then
Now, let denote the angle made with the positive -axis, then we have
which both imply
Thus, from and the polar coordinates of the point in Cartesian plane are
What are the Cartesian coordinates of the point whose distance from origin is and the angle made with the positive -axis is
Since the distance of point from the origin is and the angle made with the positive -axis is the Cartesian coordinates are
Thus, the answer is
The radius of the above circle is and the Cartesian coordinates of is If is what are the Cartesian coordinates of
From the cartesian coordinates of we can get the angle between and the positive -axis using the polar coordinates of
Let and be the polar coordinates of then since is the angle is established as follows:
Since the angle between and the positive -axis is the angle between and the positive -axis is
Hence, the Cartesian coordinates of are