Question

Polar Coordinates to Rectangular Coordinates Find the rectangular coordinates for the point whose polar coordinates are given.$(-1,5\pi /2)$.

Short answer

The rectangular coordinates of the point $(-1,5\pi /2)$are.$(0,-1)$

Step-by-step solution

Step 1.Given information.

The polar coordinates of the point are$(-1,5\pi /2)$ .

Step 2. Finding the value of x co-ordinate

Since the polar coordinates of the point are $(-1,5\pi /2)$,We can say that$r=-1$and

$\begin{array}{l}\theta =\frac{5\pi }{2}\\ \Rightarrow x=r\cos \theta \\ \Rightarrow x=-1\cos \left(\frac{5\pi }{2}\right)\\ \Rightarrow x=-1\cdot 0\\ \Rightarrow x=0\end{array}$

Step3. Finding the value of y co-ordinate

Now, to find the value of y,

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