Question

Can you help me find the polar coordinates of each rectangular coordinates
(4,0)
(0,3)
(2,2)

Answer 1

notice, they're just x,y coordinate values
thus, plot them in a cartesian plane grid

get the distance, that'd be "r"
get the angle, that'd be \(\theta\)

then plug the values for the polar coordinates using that :)

Answer 2

usually you'd need to use the tangent function to get the angle
but in this case, is too simple

Answer 3

so will the first one be (4,0 degrees)

Answer 4

well.... plot here

Answer 5

yeap... so r = 4 and angle is 0

so 4, 0 is the polar

Answer 6

what equation would I use

Answer 7

notice, the angle is 90 degrees and the distance is 3

Answer 8

hmm what equation? for.... well.. that was the 1st one, (4,0) in rectangular is the same in polar

Answer 9

ok Next one would be (3,90 degrees)

Answer 10

0, 3 has an r = 3, and an angle of \(\frac{\pi }{2}\)

Answer 11

yeap or \(\bf (3,\frac{\pi }{2})\)

Answer 12

next one would be (2sqrt(2), 45 degrees)

Answer 13

now... 2.2.... well..

hmmm yeap, that's correct
\(\bf r=\sqrt{x^2+y^2}\implies r=\sqrt{2^2+2^2}\implies r=\sqrt{8}\implies r=2\sqrt{2}
\\ \quad \\
\theta=tan^{-1}\left( \cfrac{y}{x} \right)\implies \theta=tan^{-1}\left( \cfrac{\cancel{2}}{\cancel{2}} \right)\)