Answer
(a) We can see the point plotted on the graph below.
(b) We can write two pairs of polar coordinates for this point:
$(2, 135^{\circ})$
$(-2, 315^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9bdbdbd1-3116-4fd4-8f2e-1224c1c15e9e/result_image/1529391922.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012743Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=46ca06219f092d57a6239c78a56183bbd1249e3150966154c12c50cf9a609381)
Work Step by Step
$(-\sqrt{2}, \sqrt{2})$
(a) We can see the point plotted on the graph below.
(b) $r = \sqrt{(-\sqrt{2})^2+(\sqrt{2})^2} = 2$
We can find the angle $\phi$ above the negative x-axis:
$tan~\phi = \frac{\sqrt{2}}{\sqrt{2}}$
$\phi = arctan(\frac{\sqrt{2}}{\sqrt{2}})$
$\phi = 45^{\circ}$
We can write two pairs of polar coordinates for this point:
$(2, 135^{\circ})$
$(-2, 315^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9bdbdbd1-3116-4fd4-8f2e-1224c1c15e9e/steps_image/small_1529391922.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012743Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e666fbeb5f7e8d90985fe99ce33ad0d6af36e4ef7b0cf6067a974faa55667205)