# Converting radians to degrees, help!

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.

## Answers and Replies

Hurkyl
Staff Emeritus
Gold Member
$4 \sqrt{3}$ isn't an angle...

chroot
Staff Emeritus
Gold Member
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
Staff Emeritus
Gold Member
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);
opposite angle (8,120). is this correct?

thanks again!

Hurkyl
Staff Emeritus
Gold Member
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
Staff Emeritus