Question

Polar Coordinates to Rectangular Coordinates Find the rectangular coordinates for the point whose polar coordinates are given..$(\sqrt{2},-\pi /4)$

Short answer

The rectangular coordinates of the point $(\sqrt{2},-\pi /4)$are.$(1,-1)$

Step-by-step solution

Step 1.Given information.

The polar coordinates of the point are$(\sqrt{2},-\pi /4)$

Step 2. Finding the value of x co-ordinate

Since the polar coordinates of the point are$(\sqrt{2},-\frac{\pi }{4})$,We can say that$r=\sqrt{2}$and

$\begin{array}{l}\theta =-\frac{\pi }{4}\\ \Rightarrow x=r\cos \theta \\ \Rightarrow x=\sqrt{2}\cos (-\frac{\pi }{4})\\ \Rightarrow \sqrt{2}\cdot \left(\frac{\sqrt{2}}{2}\right)\\ x=1\end{array}$

Step3. Finding the value of y co-ordinate

Now, to find the value of y,

$\begin{array}{l}\Rightarrow y=r\sin \theta \\ \Rightarrow y=\sqrt{2}\sin \left(\frac{-\pi }{4}\right)\\ \Rightarrow y=\sqrt{2}\cdot (-\frac{\sqrt{2}}{2})\\ \Rightarrow y=-1\end{array}$