Question

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

Short answer

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

Step-by-step solution

Step 1. Given information

We have been given statement:

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

We have to fill in the blanks.

Step 2. Complete the statement using transformation

Polar coordinates $(r,\theta )$of a point are related to its rectangular coordinates $(x,y)$as:

$$\begin{gathered} r=\sqrt{x^2+y^2} \\ x=r\cos \theta \\ y=r\sin \theta \end{gathered}$$