Polar Coordinates

Polar coordinates are a system of coordinates used to locate a point in a plane by its distance from a fixed point (the pole) and the angle it makes with a fixed axis (the polar axis).

Representation

A point is represented in polar coordinates as (r, θ), where r is the distance from the pole and θ is the angle measured from the polar axis in the counterclockwise direction.

Converting from Cartesian to Polar Coordinates

To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), you can use the following formulas:

• r = sqrt(x^2 + y^2)
• θ = arctan(y / x)

Converting from Polar to Cartesian Coordinates

To convert from polar coordinates (r, θ) to Cartesian coordinates (x, y), you can use the following formulas:

• x = r * cos(θ)
• y = r * sin(θ)

Graphing in Polar Coordinates

When graphing in polar coordinates, the angle θ is plotted counterclockwise from the polar axis, and the distance r determines the distance from the pole.

Practice Problems

1. Convert the point (3, 4) from Cartesian coordinates to polar coordinates.
2. Convert the point (2, π/6) from polar coordinates to Cartesian coordinates.
3. Graph the point (5, π/4) in polar coordinates.

Hope this helps! Let me know if you have any questions!