Question

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

Answer 1

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

Answer 2

whats with the ....?

Answer 3

polar solutions eh...

Answer 4

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?

Answer 5

ya polar (r, (theta))

Answer 6

cos(t) = 1-cos(t)

2cos(t) = 1

Answer 7

yup and u get 1/2 = r

Answer 8

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

Answer 9

cos(t) = 1/2

60 and 120 right? but theres a trick about polars if I aint mistaken

gotta rotate backwards or something

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

cos^1(1/2)=your answer

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

same as 240 would be too

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

pi/12 is 15 degrees right?

Answer 27

correct

Answer 28

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

Answer 29

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

Answer 30

15(5) = 75 got no idea about this one lol

15(9) = 135 = 90+45 Q2

Answer 31

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

Answer 32

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

Answer 33

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