Polar coordinates
Like any other coordinate, a polar coordinate describes a position on a 2D plane.
A polar coordinate is described by:
- the distance from the origin
- the bearing of the point from the origin
Describing the bearing
We usually use radians to describe the bearing of a polar point from the origin, but technically we could also use degrees.
The bearing starts from the line which extends from the origin to the right: called the initial line On a cartesian system, this would be the ‘positive X’ line.
Common bearings
Knowing that the bearing starts from the line extending to the right, we can say that:
- The line going to the right from the origin is at a bearing of
0\pi radians - The line going upwards from the origin is at a bearing of
\frac12\pi radians - The line going to the left from the origin is at a bearing of
\pi radians - The line going downwards from the origin is at a bearing of
\frac32\pi radians
More simply in a table:
| Line | Bearing (rad) |
|---|---|
| Right | |
| Top | |
| Left | |
| Bottom |
Format of a polar coordinate
We write the polar coordinate in the form
r is the distance from the origin\theta is the bearing of the point from the origin, measured in radians- It’s usually between
0 and2\pi
- It’s usually between
flashcards
| Question | Answer |
|---|---|
| What is a polar coordinate? | A polar coordinate describes a position on a 2D plane using the distance from the origin and the bearing from the origin. |
| What two pieces of information describe a polar coordinate? | The distance ( |
| What unit is usually used to describe the bearing of a polar point? | Radians. |
| What is the name of the line from which the bearing is measured in polar coordinates? | The initial line. |
| On a cartesian system, what does the initial line correspond to? | The ‘positive X’ line. |
| What is the bearing of the line going to the right from the origin? | |
| What is the bearing of the line going upwards from the origin? | |
| What is the bearing of the line going to the left from the origin? | |
| What is the bearing of the line going downwards from the origin? | |
| How is a polar coordinate written? | In the form |
| What does | The distance from the origin. |
| What does | The bearing of the point from the origin, measured in radians. |
| What is the usual range for | Between |