Polar Coordinate System

This week, we learned about a new system of graphing. Originally, we used the rectangular graphing system, but now we can use the polar graphing system.

On a rectangular graph, a point is defined by (x, y). To reach this point, you must travel x units to the right and y units up. No point can be defined by two different ordered pairs; for example, the point (1, 6) can only be defined by (1, 6).

On a polar graph, a point is defined by (r, θ). To reach this point, you must travel r units in the direction of θ radians. This means that a point can be defined by multiple different ordered pairs; for example, the point (2, π) can also be defined by (-2, 0). This is because traveling 2 units in the direction π is the same as traveling 2 units backwards from the direction 0 or 2π.

To convert from polar to rectangular coordinates, use the following equations:

x = r cosθ
y = r sinθ

To convert from rectangular to polar coordinates, use the following equations:

tanθ = y / x
r² = x² + y²


Next, we will learn about graphing lines on polar graphs!