Question

Determine the Cartesian coordinates of the points with polar coordinates (\sqrt{2}, \pi/4 ), (0, \pi), (-1,400\pi), and ( 2\sqrt{3},- 2\pi / 3)

Answer 1

Answer:

Step-by-step explanation:

We have the conversion from polar coordinates to cartesian as

x =rcost and y = rsint where (r,t) are the polar coordinates

Also all trignometric functions are periodic with period = 2pi

Using this we find out

$(\sqrt{2}, \pi/4 ) = (\sqrt{2}cos \pi/4, \sqrt{2}cos \pi/4,)=(1,1)\\ (0, \pi), (-1,400\pi),=(0 cos 1400 \pi, 0 sin 1400\pi)\\= (0, 0)\\\\ ( 2\sqrt{3},- 2\pi / 3) = (2\sqrt{3}, cos2\pi / 3, 2\sqrt{3},sin2\pi / 3))\\=(-\sqrt{3}, 3)$

Thus we converted polar to rectangular coordinates.

Reverse would be

from (x,y) to (r,t) as

$r=\sqrt{x^2+y^2} \\tant = y/x$