Question

How do you convert `x^2+y^2=9` into polar form?

Answer 1

Use the substitutions `x = rcos(theta)` and `y = rsin(theta)`

Explanation:

Use the substitutions `x = rcos(theta)` and `y = rsin(theta)`
Then the equation becomes
`r^2cos^2(theta) + r^2sin^2(theta) = 9`
`r^2(cos^2(theta) + sin^2(theta) ) = 9`
Because we know that `cos^2(theta) + sin^2(theta) = 1`
this gives `r^2 = 9` and hence `r= 3`