Question

Polar Coordinates to Rectangular Coordinates Find the rectangular coordinates for the point whose polar coordinates are given.$(6\sqrt{2},11\pi /6)$.

Short answer

The rectangular coordinates of the point$(6\sqrt{2},11\pi /6)$ are.$(3\sqrt{6},-3\sqrt{2})$

Step-by-step solution

Step 1.Given information.

The polar coordinates of the point are$(6\sqrt{2},11\pi /6)$

Step 2. Finding the value of x co-ordinate

Since the polar coordinates of the point are $(6\sqrt{2},11\pi /6)$we can say that$r=6\sqrt{2}$and

$\begin{array}{l}\theta =\frac{11\pi }{6}\\ \Rightarrow x=r\cos \theta \\ \Rightarrow x=6\sqrt{2}\cos \left(\frac{11\pi }{6}\right)\\ \Rightarrow x=6\sqrt{2}\cdot \left(\frac{\sqrt{3}}{2}\right)\\ \Rightarrow x=3\sqrt{6}\end{array}$

Step3. Finding the value of y co-ordinate

Now, to find the value of y,

$\begin{array}{l}\Rightarrow y=r\sin \theta \\ \Rightarrow y=6\sqrt{2}\sin \left(\frac{11\pi }{6}\right)\\ \Rightarrow y=6\sqrt{2}\cdot (-\frac{1}{2})\\ \Rightarrow y=-3\sqrt{2}\end{array}$