Question

Polar Coordinates to Rectangular Coordinates Find the rectangular coordinates for the point whose polar coordinates are given.$(5,5\pi )$.

Short answer

The rectangular coordinates of the point $(5,5\pi )$are.$(-5,0)$

Step-by-step solution

Step 1.Given information.

The polar coordinates of the point are $(5,5\pi )$.

Step 2. Finding the value of x co-ordinate

Since the polar coordinates of the point are $(5,5\pi )$we can say that$r=5$and

$\begin{array}{l}\theta =5\pi \\ \Rightarrow x=r\cos \theta \\ \Rightarrow x=5\cos \left(5\pi \right)\\ \Rightarrow x=5\cdot (-1)\\ \Rightarrow x=-5\end{array}$

Step3. Finding the value of y co-ordinate

Now, to find the value of y,

$\begin{array}{l}\Rightarrow y=r\sin \theta \\ \Rightarrow y=5\sin \left(5\pi \right)\\ \Rightarrow y=5\cdot \left(0\right)\\ \Rightarrow y=0\end{array}$