Question

How do you convert `r = 5 cos (t)` to rectangular form?

Answer 1

`r=5cost->r*r=r*5cost->r^2=5rcost->x^2+y^2=5x->x^2-5x+y^2=0->(x-5/2)^2+y^2=25/4`

Explanation:

Multiply both sides by r then use the formula `r^2=x^2+y^2, x=rcostheta` to change from polar to rectangular. Put everything on one side and complete the square to find the answer.