At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
r=r...cos(theta) = 1-cos(theta)...2cos(theta)=1...cos(theta)=(1/2)...cos^-1(1/2)=pi/3...
whats with the ....?
polar solutions eh...
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?
ya polar (r, (theta))
cos(t) = 1-cos(t) 2cos(t) = 1
yup and u get 1/2 = r
so its a 60 degree angle and if u go to 360 its also the 300 degree angle?
cos(t) = 1/2 60 and 120 right? but theres a trick about polars if I aint mistaken gotta rotate backwards or something
120 doesn't work cuz then it would be -1/2
lol..... yeah, my stupidity there :)
sooo the r either way is 1/2 and then its just the 60 and 300 but in radian form??
since -r is the same but pi off, there might be more solutions....
well the answer book said what i posted earlier.. and thats what i got.. (mostly double checking with you all)
(-1/2,120) would be a solution right?
it cant... since r is positive 1/2 not negative but that is a legit answer if that was needed
same as 240 would be too
polars are tricky because they are defined by more than 1 solution :) unlike cartiseans. but I hear ya ;)
well i got another quick question just like this one... r=cos3(theta) and r = sin3(theta)
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
if you set them eqaul to one another you ill get 1=tan3(theta)
cos and sin are equal at 45 degrees; so I would gander it has to do with muliples of 45/3
actually i have the answers for this too and its (pi/12) (5pi/12) and (9pi/12)
pi/12 is 15 degrees right?
15(3) = 45...yay!! I was close to being right lol
oh boy not sure if i should congratz u on that or a lucky guess. alright what bout the others tho
15(5) = 75 got no idea about this one lol 15(9) = 135 = 90+45 Q2
ya those are all right but how the hey are u pulling them out of no where?
if I knew what the voices in my head were hiding from me..id be alooooot smarter ;)
haha alright i understand. i have that prob too so i hear ya out on that