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|dw:1441322582245:dw|
Thats what i thought

this example too seems to be adding when i thought arg (theta) is positive
\[-\pi < \theta \le \pi \]

unless im just confused.

im still confused

that has to be the ugliest circle i have ever seen

correct answer though

Umm no that's not a circle

I was trying to show that when the Arg theta value is between 0 and 180deg then it's positive

|dw:1441326450077:dw|
your point is in the 4th quadrant

|dw:1441326527937:dw|

Yes so should it be a negative and I got negative pi/3

|dw:1441326541656:dw|

right -pi/3 is right

but

Why haa the model answera added 3pi/2 to pi/3

it looks like they wanted you to write theta in between 0 and 2pi based on their answer

so you just do -pi/3+2pi

this will put you between 0 and 2pi

i see you wanted to add pi for some reason but that would put you in the second quadrant

|dw:1441326754891:dw|
doing theta+pi will put you in second quadrant as you can see

and we definitely want to be in 4th

theta+2pi would get us back there to fourth quadrant

If the question doesn't specify will -pi/3 also be a sufficient answer

Also can u look at the image I have attached above...I guess they have demonstrated both methods

\[(r,\theta)=(r,\theta+2 \pi n) \\ \text{ or } \\ (r,\theta)=(-r,\theta+\pi+2 \pi n)\]

when it comes to polar coordinates there is not a unique way to express one point

not a unique way meaning there are infinite amount of ways to express one point

so you could haven chosen (-2,2pi/3)

on account of sine and cosine are periodic functions with period \(2\pi\)

or (2,5pi/3)
or (2,-pi/3)

and so on