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anonymous

  • one year ago

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°)

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  1. cwrw238
    • one year ago
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    Hint the point is in the 4th quadrant

  2. dumbcow
    • one year ago
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    |dw:1440031939497:dw|

  3. anonymous
    • one year ago
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    I'm not sure what you mean. I have never worked with this kind of problem before..

  4. dumbcow
    • one year ago
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    |dw:1440032084293:dw|

  5. dumbcow
    • one year ago
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    ok when converting to polar form use following equations for given point (x,y) \[r = \sqrt{x^2 + y^2}\] \[\tan \theta = \frac{y}{x}\]

  6. anonymous
    • one year ago
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    Okay so polar coordinates are the opposite coordinates?

  7. anonymous
    • one year ago
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    Okay

  8. anonymous
    • one year ago
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    so \[r=\sqrt{5^2+(-5^2)}\]

  9. anonymous
    • one year ago
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    therefore r= \[\sqrt{50}\]

  10. dumbcow
    • one year ago
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    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

  11. dumbcow
    • one year ago
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    correct, simplify the radical \[\sqrt{50} = 5 \sqrt{2}\]

  12. anonymous
    • one year ago
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    Alright, and I got \[\tan \theta=-5/5\]

  13. anonymous
    • one year ago
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    =-1

  14. anonymous
    • one year ago
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    theta = tan^-1(-1)

  15. anonymous
    • one year ago
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    so theta= -pi/4

  16. anonymous
    • one year ago
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    What am I to do with this information?

  17. dumbcow
    • one year ago
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    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

  18. anonymous
    • one year ago
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    I dont understand..I can see the equivalent angle

  19. anonymous
    • one year ago
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    I just dont know how to get it

  20. dumbcow
    • one year ago
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    here is a general form showing all 4 possible points for a given (x,y) \[(r,\theta)\] \[(r, \theta +2\pi)\] \[(-r, \theta + \pi)\] \[(-r, \theta - \pi)\]

  21. dumbcow
    • one year ago
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    |dw:1440033135732:dw|

  22. anonymous
    • one year ago
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    So what would be my theta and my r?

  23. dumbcow
    • one year ago
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    you already calculated those ..... r = sqrt(50) , theta = pi/4

  24. dumbcow
    • one year ago
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    sorry -pi/4

  25. anonymous
    • one year ago
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    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. \[-5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)-pi\]

  26. anonymous
    • one year ago
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    what do you mean by 'find 2 match the given pairs'

  27. dumbcow
    • one year ago
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    figure it out...gotta go good luck!

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