Cartesian to polar coordinates

If we have a Cartesian coordinate in the form , then we can convert these to a polar coordinate, using our polar coordinate identities from before!

General steps

Polar coordinates are in the form , where:

• is the magnitude, the distance of a point from the origin
• is the bearing from the origin, starting from the right-stretching line and going anticlockwise.

To find the magnitude of the polar coordinate, :

• Just use the Pythagorean theorem to find the hypotenuse!

Then to find the angle, :

Note: If the coordinate is negative, we need to add to our answer for . That’s because, otherwise, the angle we got from would be in the wrong quadrant.

Find the polar coordinate from the Cartesian

• Answer:

Convert the cartesian coordinate to polar coordinates (to 3sf)

• Because our coordinate is negative, we need to add :
• Answer:

Convert the cartesian coordinate to polar coordinates (to 3sf)

• Because our coordinate is negative, we need to add
• Answer:

Convert the cartesian coordinate to polar coordinates (to 3sf)

• Because our coordinate is positive, we don’t need to add !
• Answer:

Write as a set of polar coordinates

• Answer: