Question

Rectangular Coordinates to Polar Coordinates Convert the rectangular coordinates to polar coordinates with$r>0$ and$0\le \theta <2\pi .$$(-1,1)$.

Short answer

The polar coordinates of the point $(-1,1)$are.$(\sqrt{2},\frac{3\pi }{4})$

Step-by-step solution

Step 1.Given information.

The polar coordinates of the point are $(-1,1)$.

Step 2.Since the rectangular coordinates of the point are (-1,1)

$\begin{array}{l}\Rightarrow r^2=x^2+y^2\\ \Rightarrow r^2\text{Invalid <m:msup> element}=+1^2\\ \Rightarrow r^2=2\\ \Rightarrow r=\pm \sqrt{2}\end{array}$

Since$r>0$ , the value of is taken as$+\sqrt{2}$

Step3. Finding the value of angle

Now, to find the value of$\theta$,

$\begin{array}{l}\Rightarrow \tan \theta =\frac{y}{x}\\ \Rightarrow \tan \theta =\frac{-1}{1}\\ \Rightarrow \theta ={\tan }^{-1}(-1)\\ \Rightarrow \theta =\frac{3\pi }{4},\frac{7\pi }{4}\text{inthegivenrange}0<\theta <2\pi \end{array}$