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anonymous

  • 5 years ago

How do you find the points of intersection of r = cos(theta) and r =1-cos(theta)?

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  1. anonymous
    • 5 years ago
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    r=r...cos(theta) = 1-cos(theta)...2cos(theta)=1...cos(theta)=(1/2)...cos^-1(1/2)=pi/3...

  2. anonymous
    • 5 years ago
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    whats with the ....?

  3. amistre64
    • 5 years ago
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    polar solutions eh...

  4. anonymous
    • 5 years ago
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    the answers are (1/2, pi/3) and (1/2, 5pi/3) Do you basically set them equal to each other then you shall get cos(theta)= 1/2 then just plug the 1/2 back into the r equations?

  5. anonymous
    • 5 years ago
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    ya polar (r, (theta))

  6. amistre64
    • 5 years ago
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    cos(t) = 1-cos(t) 2cos(t) = 1

  7. anonymous
    • 5 years ago
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    yup and u get 1/2 = r

  8. anonymous
    • 5 years ago
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    so its a 60 degree angle and if u go to 360 its also the 300 degree angle?

  9. amistre64
    • 5 years ago
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    cos(t) = 1/2 60 and 120 right? but theres a trick about polars if I aint mistaken gotta rotate backwards or something

  10. anonymous
    • 5 years ago
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    120 doesn't work cuz then it would be -1/2

  11. amistre64
    • 5 years ago
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    lol..... yeah, my stupidity there :)

  12. anonymous
    • 5 years ago
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    sooo the r either way is 1/2 and then its just the 60 and 300 but in radian form??

  13. anonymous
    • 5 years ago
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    cos^1(1/2)=your answer

  14. amistre64
    • 5 years ago
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    since -r is the same but pi off, there might be more solutions....

  15. anonymous
    • 5 years ago
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    *cos^-1(1/2)=your answer

  16. anonymous
    • 5 years ago
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    well the answer book said what i posted earlier.. and thats what i got.. (mostly double checking with you all)

  17. amistre64
    • 5 years ago
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    (-1/2,120) would be a solution right?

  18. anonymous
    • 5 years ago
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    it cant... since r is positive 1/2 not negative but that is a legit answer if that was needed

  19. anonymous
    • 5 years ago
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    same as 240 would be too

  20. amistre64
    • 5 years ago
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    polars are tricky because they are defined by more than 1 solution :) unlike cartiseans. but I hear ya ;)

  21. anonymous
    • 5 years ago
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    well i got another quick question just like this one... r=cos3(theta) and r = sin3(theta)

  22. anonymous
    • 5 years ago
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    it's 1/2, pi/3...1/2, pi/5...because cos(pi/3) = 1/2...cos(pi/5) = 1/2...and it keeps going because it's periodic

  23. anonymous
    • 5 years ago
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    if you set them eqaul to one another you ill get 1=tan3(theta)

  24. amistre64
    • 5 years ago
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    cos and sin are equal at 45 degrees; so I would gander it has to do with muliples of 45/3

  25. anonymous
    • 5 years ago
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    actually i have the answers for this too and its (pi/12) (5pi/12) and (9pi/12)

  26. amistre64
    • 5 years ago
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    pi/12 is 15 degrees right?

  27. anonymous
    • 5 years ago
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    correct

  28. amistre64
    • 5 years ago
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    15(3) = 45...yay!! I was close to being right lol

  29. anonymous
    • 5 years ago
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    oh boy not sure if i should congratz u on that or a lucky guess. alright what bout the others tho

  30. amistre64
    • 5 years ago
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    15(5) = 75 got no idea about this one lol 15(9) = 135 = 90+45 Q2

  31. anonymous
    • 5 years ago
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    ya those are all right but how the hey are u pulling them out of no where?

  32. amistre64
    • 5 years ago
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    if I knew what the voices in my head were hiding from me..id be alooooot smarter ;)

  33. anonymous
    • 5 years ago
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    haha alright i understand. i have that prob too so i hear ya out on that

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