Answer
$(4, \frac{3\pi}{2})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(4, -\frac{\pi}{2})$
$(-4, \frac{\pi}{2})$
(c) $(x,y) = (0, -4)$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/7b9a545e-2ff8-4d8e-b66c-24612b3a5168/result_image/1529335079.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015216Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=beaba2348bfed399f745d453cba4efade5f0a25d8be26c2c03328764525e202f)
Work Step by Step
$(4, \frac{3\pi}{2})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(4, -\frac{\pi}{2})$
$(-4, \frac{\pi}{2})$
(c) We can find the rectangular coordinates:
$r = 4$ and $\theta = \frac{3\pi}{2}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (4~cos~\frac{3\pi}{2}, 4~sin~\frac{3\pi}{2})$
$(x,y) = (0, -4)$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/7b9a545e-2ff8-4d8e-b66c-24612b3a5168/steps_image/small_1529335079.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015216Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=24d43fb37e1b7dbd25183f0f563c14481a10b6900df52e62d3173af425cabd39)