anonymous
  • anonymous
How do you find the points of intersection of r = cos(theta) and r =1-cos(theta)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
r=r...cos(theta) = 1-cos(theta)...2cos(theta)=1...cos(theta)=(1/2)...cos^-1(1/2)=pi/3...
anonymous
  • anonymous
whats with the ....?
amistre64
  • amistre64
polar solutions eh...

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anonymous
  • anonymous
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?
anonymous
  • anonymous
ya polar (r, (theta))
amistre64
  • amistre64
cos(t) = 1-cos(t) 2cos(t) = 1
anonymous
  • anonymous
yup and u get 1/2 = r
anonymous
  • anonymous
so its a 60 degree angle and if u go to 360 its also the 300 degree angle?
amistre64
  • amistre64
cos(t) = 1/2 60 and 120 right? but theres a trick about polars if I aint mistaken gotta rotate backwards or something
anonymous
  • anonymous
120 doesn't work cuz then it would be -1/2
amistre64
  • amistre64
lol..... yeah, my stupidity there :)
anonymous
  • anonymous
sooo the r either way is 1/2 and then its just the 60 and 300 but in radian form??
anonymous
  • anonymous
cos^1(1/2)=your answer
amistre64
  • amistre64
since -r is the same but pi off, there might be more solutions....
anonymous
  • anonymous
*cos^-1(1/2)=your answer
anonymous
  • anonymous
well the answer book said what i posted earlier.. and thats what i got.. (mostly double checking with you all)
amistre64
  • amistre64
(-1/2,120) would be a solution right?
anonymous
  • anonymous
it cant... since r is positive 1/2 not negative but that is a legit answer if that was needed
anonymous
  • anonymous
same as 240 would be too
amistre64
  • amistre64
polars are tricky because they are defined by more than 1 solution :) unlike cartiseans. but I hear ya ;)
anonymous
  • anonymous
well i got another quick question just like this one... r=cos3(theta) and r = sin3(theta)
anonymous
  • anonymous
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
anonymous
  • anonymous
if you set them eqaul to one another you ill get 1=tan3(theta)
amistre64
  • amistre64
cos and sin are equal at 45 degrees; so I would gander it has to do with muliples of 45/3
anonymous
  • anonymous
actually i have the answers for this too and its (pi/12) (5pi/12) and (9pi/12)
amistre64
  • amistre64
pi/12 is 15 degrees right?
anonymous
  • anonymous
correct
amistre64
  • amistre64
15(3) = 45...yay!! I was close to being right lol
anonymous
  • anonymous
oh boy not sure if i should congratz u on that or a lucky guess. alright what bout the others tho
amistre64
  • amistre64
15(5) = 75 got no idea about this one lol 15(9) = 135 = 90+45 Q2
anonymous
  • anonymous
ya those are all right but how the hey are u pulling them out of no where?
amistre64
  • amistre64
if I knew what the voices in my head were hiding from me..id be alooooot smarter ;)
anonymous
  • anonymous
haha alright i understand. i have that prob too so i hear ya out on that

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