Question

Polar Coordinates to Rectangular Coordinates A point is graphed in polar form. Find its rectangular coordinates.

Short answer

The rectangular coordinates of$S(2,\frac{5\pi }{6})$ are.${(-\sqrt{3},1)}^{.}$

Step-by-step solution

Step 1.Given information.

From the figure, the polar coordinates of the point s are $(2,\frac{5\pi }{6})$.

Step 2. We can find the rectangular coordinates of the point using the polar to rectangular coordinates conversion formulas.

Since the polar coordinates of S are $(2,\frac{5\pi }{6})$, we can say that $r=2$and

$\begin{array}{l}\theta =\frac{5\pi }{6}.\\ \Rightarrow x=r\cos \theta \\ \Rightarrow x=2\cos \left(\frac{5\pi }{6}\right)\\ \Rightarrow x=2\cdot (-\frac{\sqrt{3}}{2})\\ \Rightarrow x=-\sqrt{3}\end{array}$

Now, to find the value of y,

$\begin{array}{l}\Rightarrow y=r\sin \theta \\ \Rightarrow y=2\sin \left(\frac{5\pi }{6}\right)\\ \Rightarrow y=2\cdot \left(\frac{1}{2}\right)\\ \Rightarrow y=1\end{array}$