Answer
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(1, -315^{\circ})$
$(-1, 225^{\circ})$
(c) $(x,y) = (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/5d790c7a-ec75-4a12-a3fa-90c8a80d6db0/result_image/1529295987.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T011446Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2a02ae323e30aeeda87d8d880f85f6c5c3faadc17122f0f2ab4dd583c8ac85fe)
Work Step by Step
(a) We can see the point plotted on the graph below.
(b) $(1, 45^{\circ})$
We can write two other pairs of polar coordinates for this point:
$(1, -315^{\circ})$
$(-1, 225^{\circ})$
(c) We can find the rectangular coordinates:
$r = 1$ and $\theta = 45^{\circ}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (1~cos~45^{\circ}, 1~sin~45^{\circ})$
$(x,y) = (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/5d790c7a-ec75-4a12-a3fa-90c8a80d6db0/steps_image/small_1529295987.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T011446Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=6ca79f3bf074f10df2a984265fb400b6522268ed9ea2c54ba68fba24a9fa76de)