How do you convert r = 1 + cos (theta) into rectangular form?

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Answer 1 · 2017-07-05T03:17:24

#x^2+y^2 =sqrt(x^2+y^2) + x#

Converting from polar to rectangular form:

#x = r cos(theta)#, #y = r sin(theta)#

#x^2+y^2=r^2 -> r=sqrt(x^2+y^2)#

Here our polar equation is: #r = 1 + cos(theta)#

Multiply both sides by #r -> r^2 = r(1+cos(theta))#

#:.r^2 = r + rcos(theta)#

Substituting for #r, r^2 and rcos(theta)# yields:

#x^2+y^2 =sqrt(x^2+y^2) + x#

Which is our polar equation in rectangular form.

NB: This is the equation of the cardioid below.

graph{ x^2+y^2 =sqrt(x^2+y^2) + x [-1.835, 4.325, -1.478, 1.602]}