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anonymous

  • 5 years ago

convert to polar form. x^2=8y

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  1. anonymous
    • 5 years ago
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    x=rcos(theta) y=rsin(theta)

  2. anonymous
    • 5 years ago
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    r^2cos^2(theta)=8rsin(theta)

  3. anonymous
    • 5 years ago
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    so its r=8sin(theta)/cos^2(theta)?

  4. anonymous
    • 5 years ago
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    right

  5. anonymous
    • 5 years ago
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    so the answer is in r= form when there are no set points. But with set points you write it as (r, theta) ?

  6. anonymous
    • 5 years ago
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    I don't know what you mean by set points. In polar form there is a magnitude and a direction/angle.

  7. anonymous
    • 5 years ago
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    and i'd rather not write up a new question for these, but im also struggling the other way around. converting polar to rectangular. 1) r^2*cos(2theta)=1 2)r=2cos(theta)-4sin(theta) think you can help out?

  8. anonymous
    • 5 years ago
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    by set points in meant (1,4) or something to that extent. I was able to answer that though.

  9. anonymous
    • 5 years ago
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    when you run into something with a coefficient of theta use your trig identities to get rid of it so you can use x=rcos(theta) y=rsin(theta) to convert back to rectangular.

  10. anonymous
    • 5 years ago
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    actually i have 2. and what trig identity would i use here? cos(2A) = cos²A − sin² ?

  11. anonymous
    • 5 years ago
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    half angle

  12. anonymous
    • 5 years ago
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    cos(A/2)

  13. anonymous
    • 5 years ago
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    im not sure how this applies if i have r^2 * cos(2*theta)

  14. anonymous
    • 5 years ago
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    cos(theta/2)= sqrt((1+cos(theta))/2)

  15. anonymous
    • 5 years ago
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    actually you were right, you don't use the half angle...

  16. anonymous
    • 5 years ago
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    you use the one that matches, double angle.

  17. anonymous
    • 5 years ago
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    there are 3 for cosine, i cant tell which one would work in this scenario

  18. anonymous
    • 5 years ago
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    cos(2a)=cos^2*a)+sin^2(a)

  19. anonymous
    • 5 years ago
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    when you put that one in you'll end up with two terms both multiplied by r^2

  20. anonymous
    • 5 years ago
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    then you can simply substitute them for x^2 and y^2

  21. anonymous
    • 5 years ago
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    so I'm at r^2cos^2(theta)- r^2sin^2(theta)=1. which turns to x^2-y^2=1...and thats the answer on the sheet. Got it, thanks!

  22. anonymous
    • 5 years ago
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    You're welcome

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