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wampominater

  • one year ago

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

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  1. wampominater
    • one year ago
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    so right now I have \[\cos(\theta) = \frac{ 4 }{ 4\sqrt{2} }\] and \[\sin(\theta)=-\frac{ 4 }{ 4\sqrt{2} }\] but i dont know where to go from here... please help!

  2. jim_thompson5910
    • one year ago
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    the 4's cancel leaving with 1 over sqrt(2) for the first fraction

  3. jim_thompson5910
    • one year ago
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    \[\Large \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}\]

  4. wampominater
    • one year ago
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    alright, but how do i make that a polar coordinate. i need to take the arc sin according to the examples in my book but that doesnt work here

  5. wampominater
    • one year ago
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    and the arc cos

  6. jim_thompson5910
    • one year ago
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    you can use the unit circle

  7. wampominater
    • one year ago
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    oh wait cause now they are known values on the unit circle

  8. jim_thompson5910
    • one year ago
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    look on the unit circle where the x coordinate is \(\Large \frac{1}{\sqrt{2}}\) or \(\Large \frac{\sqrt{2}}{2}\)

  9. wampominater
    • one year ago
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    315

  10. wampominater
    • one year ago
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    ok so the first polar coordinate would be \[\left( 4\sqrt{2} , 315\right)\]

  11. jim_thompson5910
    • one year ago
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    yes

  12. wampominater
    • one year ago
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    how would i find a second one equal to that?

  13. jim_thompson5910
    • one year ago
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    |dw:1439180139138:dw|

  14. jim_thompson5910
    • one year ago
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    |dw:1439180155156:dw|

  15. jim_thompson5910
    • one year ago
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    Draw a line from (4,-4) through the origin |dw:1439180192858:dw|

  16. jim_thompson5910
    • one year ago
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    |dw:1439180205002:dw|

  17. wampominater
    • one year ago
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    so that would be 135 degrees?

  18. jim_thompson5910
    • one year ago
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    yes so another polar point would be \(\Large \left( -4\sqrt{2} , 135\right)\)

  19. wampominater
    • one year ago
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    ah ok, thank you for your help!

  20. jim_thompson5910
    • one year ago
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    you start at the origin facing directly east then you turn 135 degrees counter clockwise still facing this direction, you walk backwards (hence the negative r value) 4*sqrt(2) units

  21. wampominater
    • one year ago
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    alright that makes sense

  22. wampominater
    • one year ago
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    thank you!

  23. jim_thompson5910
    • one year ago
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    no problem

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