anonymous
  • anonymous
PLEASE Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°. (5 square root of 2, 315°), (-5 square root of 2, 135°) (5 square root of 2, 45°), (-5 square root of 2, 225°) (5 square root of 2, 135°), (-5 square root of 2, 315°) (5 square root of 2, 225°), (-5 square root of 2, 45°)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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cwrw238
  • cwrw238
Hint the point is in the 4th quadrant
dumbcow
  • dumbcow
|dw:1440031939497:dw|
anonymous
  • anonymous
I'm not sure what you mean. I have never worked with this kind of problem before..

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dumbcow
  • dumbcow
|dw:1440032084293:dw|
dumbcow
  • dumbcow
ok when converting to polar form use following equations for given point (x,y) \[r = \sqrt{x^2 + y^2}\] \[\tan \theta = \frac{y}{x}\]
anonymous
  • anonymous
Okay so polar coordinates are the opposite coordinates?
anonymous
  • anonymous
Okay
anonymous
  • anonymous
so \[r=\sqrt{5^2+(-5^2)}\]
anonymous
  • anonymous
therefore r= \[\sqrt{50}\]
dumbcow
  • dumbcow
now there are multiple ways of writing a given point in polar form different angles can be used as long as tan = y/x r can be neg, which reflects the point 180 degrees
dumbcow
  • dumbcow
correct, simplify the radical \[\sqrt{50} = 5 \sqrt{2}\]
anonymous
  • anonymous
Alright, and I got \[\tan \theta=-5/5\]
anonymous
  • anonymous
=-1
anonymous
  • anonymous
theta = tan^-1(-1)
anonymous
  • anonymous
so theta= -pi/4
anonymous
  • anonymous
What am I to do with this information?
dumbcow
  • dumbcow
ok good so we have 1 angle (-45 or -pi/4) now use my circle drawings above to see how to get an equivalent angle
anonymous
  • anonymous
I dont understand..I can see the equivalent angle
anonymous
  • anonymous
I just dont know how to get it
dumbcow
  • dumbcow
here is a general form showing all 4 possible points for a given (x,y) \[(r,\theta)\] \[(r, \theta +2\pi)\] \[(-r, \theta + \pi)\] \[(-r, \theta - \pi)\]
dumbcow
  • dumbcow
|dw:1440033135732:dw|
anonymous
  • anonymous
So what would be my theta and my r?
dumbcow
  • dumbcow
you already calculated those ..... r = sqrt(50) , theta = pi/4
dumbcow
  • dumbcow
sorry -pi/4
anonymous
  • anonymous
Oh, okay. I would have the following possible answers then: A. \[5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)\] B. \[5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)+2pi\] C. \[-5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)+pi\] D. \[-5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)-pi\]
anonymous
  • anonymous
what do you mean by 'find 2 match the given pairs'
dumbcow
  • dumbcow
figure it out...gotta go good luck!

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