Converting polar angle arctan(4√3/−4) to degrees

[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.

 

[Hurkyl]

$4 \sqrt{3}$ isn't an angle...

 

[chroot]

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

 

[StarkyDee]

Ah. Inverse Tan of y/x.

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

Thanks ~Dave~

 

[Hurkyl]

Don't forget to check that your answer is in the correct quadrant!

 

[StarkyDee]

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!

 

[Hurkyl]

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...

 

[StarkyDee]

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.

 

[Hurkyl]

right.

 

[StarkyDee]

Thanks for helping me out Hurkyl, appreciated much!
Studying for finals have turned my brain into mush.