Converting radians to degrees, help

In summary, the conversation discusses converting Cartesian coordinates into polar coordinates. The speaker is looking for 3 sets of polar coordinates for the given Cartesian coordinates and uses trigonometry to solve for the angle. They also discuss the importance of checking the quadrant and the correct conversion of degrees.
  • #1
StarkyDee
I know this is an easy problem, but I need to know 3 sets of polar coordinates for the Cartesian coordinates (-4,4[itex]\sqrt{3}}[/itex])

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

How do I convert 4[itex]\sqrt{3}}[/itex]) to degrees?

(4[itex]\sqrt{3}}[/itex]) = 6.92820 Is this in radians?

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

thanks.
 
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  • #2
[itex]4 \sqrt{3}[/itex] isn't an angle...
 
  • #3
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
 
  • #4
Ah. Inverse Tan of y/x.

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

Thanks ~Dave~
 
  • #5
Don't forget to check that your answer is in the correct quadrant!
 
  • #6
well -60 degrees would be in the 4th quadrant.
but when i graph (-4,4[itex]\sqrt{3}}[/itex]) 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!
 
  • #7
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...
 
  • #8
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.
 
  • #9
right.
 
  • #10
Thanks for helping me out Hurkyl, appreciated much!
Studying for finals have turned my brain into mush.
 

FAQ: Converting radians to degrees, help

What is the formula for converting radians to degrees?

The formula for converting radians to degrees is: degrees = radians * (180 / pi).

How do I convert radians to degrees?

To convert radians to degrees, multiply the given value in radians by (180 / pi). This will give you the equivalent value in degrees.

What is the value of pi in radians?

The value of pi in radians is approximately 3.14159. However, it is more commonly represented as just "pi" in mathematical equations.

What is the difference between radians and degrees?

Radians and degrees are two different units of measuring angles. Radians are based on the radius of a circle, while degrees are based on dividing a circle into 360 equal parts.

Can I use a calculator to convert radians to degrees?

Yes, most calculators have a function that allows you to convert between radians and degrees. Make sure to check the user manual or instructions for your specific calculator to find the correct function.

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