Question 590596: How do I find the polar coordinates of these rectangular points..(Sorry about the wording I'm so confused)?
1. (-√3,-1)
2. (-1,-√3)
I attempted two easier problems so if you could check them I'd appreciate it:)
1.(5,0)--> (5,π)
2.(0,-6)--> (π,6)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You want to convert from ) to )
Use the following relationships:
)
For
)
^2\ +\ \left(-1\right)^2\ =\ 3\ +\ 1\ =\ 4\ \Rightarrow\ r\ =\ 2)
)
So
but tangent is the ratio of sine to cosine, so:
by the way, before we get too far along, notice that both  and  are negative which tells us that our point is in the third quadrant meaning that, whatever  turns out to be, we are certain that it is in the interval 
Square both sides of:
Then cross multiply:
)
A little algebra music, Sammy:
\ =\ 0)
Apply the Pythagorean Identity:
\ =\ 0)
Another chorus, Sammy:
Use the unit circle:
To see that the 3rd quadrant angle where 
is 
So the polar coordinate point is )
Do the other ones the same way, including the two that you did that are, in sum, 75% wrong.
John
My calculator said it, I believe it, that settles it
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