Answer
(a) We can see the point plotted on the graph below.
(b) We can write two pairs of polar coordinates for this point:
$(2, 45^{\circ})$
$(-2, 225^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3f2f932e-d579-4317-a20a-0873f6b5383c/result_image/1529391217.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001352Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=bbc5ac5454e88c02cbb250876bc751b5a5bf4876b4925e2da57e48dfd8d00ae9)
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 $x$ above the positive x-axis:
$tan~x = \frac{\sqrt{2}}{\sqrt{2}}$
$x = arctan(\frac{\sqrt{2}}{\sqrt{2}})$
$x = 45^{\circ}$
We can write two pairs of polar coordinates for this point:
$(2, 45^{\circ})$
$(-2, 225^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3f2f932e-d579-4317-a20a-0873f6b5383c/steps_image/small_1529391217.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001352Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e38e1c5ed99bd949c02584037ccc384f7012312d27ff541f85f0235c7f2c41fa)