Ask your own question, for FREE!
Mathematics 30 Online
OpenStudy (anonymous):

does cartesian equation of a cardiode exist??

OpenStudy (anonymous):

i believe it does

OpenStudy (anonymous):

yeah i just think its really ugly

OpenStudy (anonymous):

can it be obtained from the polar equation...?

OpenStudy (anonymous):

(x2 + y2 - 2ax)2 = 4a2(x2 + y2)

OpenStudy (anonymous):

how did u obtain it??

OpenStudy (anonymous):

the one i know, follow and see if it makes sense r = 1+sin t multiply each side by r r^2=r+rsint r^2 also = x^2+y^2 y=rsint \[x ^{2}+y ^{2}=\sqrt{x ^{2}+y ^{2}}+y\]

OpenStudy (anonymous):

r^2 = x^2 + y^2 is for circle

OpenStudy (anonymous):

yes it is but that fact still holds true in polar because: x = rcost in polar y= rsint in polar x^2 = r^2cos^2t y^2 = r^2sin^2t add x^2 +y^2= r^2cos^2t + r^2sin^2t and factor out the r^2 so x^2 + y^2 = r^2 (cos^2t + sin^2t) and the identity say cos squared plus sin squared = 1 thus x^2 +y^2 = r^2

OpenStudy (anonymous):

also x^2+y^2=√(x^2+y^2)+y which is the equation i had given above for the cartiode rearranged is y= x^2+y^2 -√(x^2+y^2) and that is not the equation for a circle. remember while cartesian is rectangular polar is circular so converting polar to cartesian will give equations that often times resemble circles

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!