Converting radians to degrees, help

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To convert the Cartesian coordinates (-4, 4√3) to polar coordinates, the hypotenuse is calculated as r = 8. The angle can be found using the inverse tangent of y/x, which gives -60 degrees, but this angle is in the fourth quadrant. Since the point lies in the second quadrant, the correct angles for the polar coordinates are (8, 120 degrees) and (8, -240 degrees). The discussion emphasizes the importance of ensuring angles correspond to the correct quadrant based on the original Cartesian coordinates.
StarkyDee
I know this is an easy problem, but I need to know 3 sets of polar coordinates for the Cartesian coordinates (-4,4\sqrt{3}})

So I graphed the points and got the hypotenuse, r = 8.

How do I convert 4\sqrt{3}}) to degrees?

(4\sqrt{3}}) = 6.92820 Is this in radians?

and do I then multiply it by (180/pi) to get degrees?

thanks.
 
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4 \sqrt{3} isn't an angle...
 
It sounds like you've already drawn a triangle -- so use trig to solve for the angle. The angle is the inverse tangent of y/x.

Why are you trying to convert the cartesian y-coordinate to degrees? That doesn't even make sense.

- Warren
 
Ah. Inverse Tan of y/x.

4\sqrt{3}}/-4 = -1.7320 = -60 degrees.

Thanks ~Dave~
 
Don't forget to check that your answer is in the correct quadrant!
 
well -60 degrees would be in the 4th quadrant.
but when i graph (-4,4\sqrt{3}}) it is only valid in the 2nd quadrant and you can't have a -60 degrees in the 2nd quad. so if i start in the 4 quadrant at -60

the 3 points would be: (8,-60);
add 360 (8,-240);
opposite angle (8,120). is this correct?

thanks again!
 
Well, tell me, how many of those are in the second quadrant?

All of your answers must be in the second quadrant because the desired point is in the second quadrant...
 
Ah. So -60 would not work because it's in the 4th quadrant. therefore (8,-60) is not a point. that makes sense.

but (8,-240) and (8,120) and (8,-600) would be in the 2nd quadrant.
 
right.
 
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Thanks for helping me out Hurkyl, appreciated much!
Studying for finals have turned my brain into mush.
 
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