Question

In converting from polar coordinates to rectangular coordinates, what formulas will you use?

Short answer

To convert polar coordinates $(r,\theta )$to rectangular coordinates $(x,y)$we use the formulas

$$\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}$$

Step-by-step solution

Step 1. Given

In a rectangular coordinate system a point in the plane is represented by an ordered pair of numbers $(x,y)$, where x and y equal the signed distance of the point from the y-axis and x-axis, respectively.

A point in a polar coordinate system is represented by an ordered pair of numbers $(r,\theta )$. If $r>0$, then r is the distance of the point from the pole; $\theta$ is an angle formed by the polar axis and a ray from the pole through the point.

Step 2. Formula Used

If P is a point with polar coordinates $(r,\theta )$, the rectangular coordinates $(x,y)$ of P are given by

$$\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}$$

Using these formulas we can convert a given polar coordinate into its equivalent rectangular coordinate.