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

- anonymous

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

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- anonymous

r=r...cos(theta) = 1-cos(theta)...2cos(theta)=1...cos(theta)=(1/2)...cos^-1(1/2)=pi/3...

- anonymous

whats with the ....?

- amistre64

polar solutions eh...

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## More answers

- 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

ya polar (r, (theta))

- amistre64

cos(t) = 1-cos(t)
2cos(t) = 1

- anonymous

yup and u get 1/2 = r

- anonymous

so its a 60 degree angle and if u go to 360 its also the 300 degree angle?

- 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

120 doesn't work cuz then it would be -1/2

- amistre64

lol..... yeah, my stupidity there :)

- anonymous

sooo the r either way is 1/2 and then its just the 60 and 300 but in radian form??

- anonymous

cos^1(1/2)=your answer

- amistre64

since -r is the same but pi off, there might be more solutions....

- anonymous

*cos^-1(1/2)=your answer

- anonymous

well the answer book said what i posted earlier.. and thats what i got.. (mostly double checking with you all)

- amistre64

(-1/2,120) would be a solution right?

- anonymous

it cant... since r is positive 1/2 not negative but that is a legit answer if that was needed

- anonymous

same as 240 would be too

- amistre64

polars are tricky because they are defined by more than 1 solution :) unlike cartiseans. but I hear ya ;)

- anonymous

well i got another quick question just like this one... r=cos3(theta) and r = sin3(theta)

- 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

if you set them eqaul to one another you ill get 1=tan3(theta)

- amistre64

cos and sin are equal at 45 degrees; so I would gander it has to do with muliples of 45/3

- anonymous

actually i have the answers for this too and its (pi/12) (5pi/12) and (9pi/12)

- amistre64

pi/12 is 15 degrees right?

- anonymous

correct

- amistre64

15(3) = 45...yay!! I was close to being right lol

- anonymous

oh boy not sure if i should congratz u on that or a lucky guess. alright what bout the others tho

- amistre64

15(5) = 75 got no idea about this one lol
15(9) = 135 = 90+45 Q2

- anonymous

ya those are all right but how the hey are u pulling them out of no where?

- amistre64

if I knew what the voices in my head were hiding from me..id be alooooot smarter ;)

- anonymous

haha alright i understand. i have that prob too so i hear ya out on that

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