for the given point in rectangular coordinates, find two sets of polar coordinates for the point (2sqrt(3),2) , 0

Question

for the given point in rectangular coordinates, find two sets of polar coordinates for the point (2sqrt(3),2) , 0<theta<2pi

el_arrow · Answer

i got r = 4 how do i get theta?

el_arrow · Answer

@SolomonZelman

jdoe0001 · Answer

right
the coordinates are (x,y)

to get the angle, recall that   tangent = y/x

el_arrow · Answer

i know theta=tan^-1(2/2sqrt(3)) but i cant figure out the angles

el_arrow · Answer

is there an easy way to this?

jdoe0001 · Answer

hmm

jdoe0001 · Answer

nope... you'd need to get the arcTangent to get $\theta$

jdoe0001 · Answer

hmmm oddly enough, is a known angle

el_arrow · Answer

would the angle be pi/3?

jdoe0001 · Answer

jdoe0001 · Answer

so...that'd be  $\bf \cfrac{\pi }{6}$

now, keep in mind that arcTangent   has a domain of $\bf -\cfrac{\pi }{2}<\theta<\cfrac{\pi }{2}$

jdoe0001 · Answer

so the other angle, will be in the 4th quadrant

el_arrow · Answer

in the 4th quadrant.....would it be 5pi/6?

jdoe0001 · Answer

well... 5/6 of $\pi$   is not even one whole $\pi$

so..to land on the 4th quadrant it has to be much more than that

el_arrow · Answer

i mean 11pi/6

jdoe0001 · Answer

keep in mind that $\bf \cfrac{6\pi }{6}\implies \pi $

jdoe0001 · Answer

yeap

el_arrow · Answer

okay so the two sets would be (4,pi/6) and (4,11pi/6)?

jdoe0001 · Answer

yeap

el_arrow · Answer

alright thanks so much for your help @jdoe0001

jdoe0001 · Answer

yw