Chapter 15.1, Problem 3MRE

To determine

Convert the rectangular coordinates into polar coordinates.

Answer to Problem 3MRE

  $\left(3,90°\right)$

Explanation of Solution

Given information:

Given: $\left(0,3\right)$

Calculation:

Here, the polar coordinates of a point are an ordered pair $\left(r,\theta \right)$ .

Now, we will use the following formula for the conversion of rectangular coordinate into polar coordinate:

  $\begin{array}{l}r=\pm \sqrt{x^2+y^2};\cos \theta =\frac{x}{r},\sin \theta =\frac{y}{r}\\ puttingx=0andy=3:\\ r=\pm \sqrt{{\left(0\right)}^2+{\left(3\right)}^2}\\ r=\pm \sqrt{9}\\ r=\pm 3\end{array}$

Now, we have observed that the given rectangular coordinates lie in the first quadrant. So, the terminal side of $\theta$ passes through the first quadrant.

  $\begin{array}{l}Now,puttingr=3andy=3in:\\ \sin \theta =\frac{y}{r}\\ \sin \theta =\frac{3}{3}\\ \sin \theta =1\\ \therefore \theta =90°\end{array}$

Hence, the polar coordinates are $\left(3,90°\right)$ .