Thread: polar to parametric equation conversion.

1. polar to parametric equation conversion.

Write the polar equation r = cos(4*theta) in the parametric form x = x(t), y = y(t)
r = cos(4*theta), x = r * cos(theta), y = r * sin(theta)

x = cos(4*t) * cos(t)

y = cos(4*t) * sin(t)

Do the functions have to be in terms of t or can they be in theta?

Am I correct?

2. I would take $\displaystyle r = cos(4\theta)$ and multiply both sides by $\displaystyle r$

this gives $\displaystyle r^2= r\times cos(4\theta)$

and using $\displaystyle r^2 = x^2+y^2$

$\displaystyle r^2= r\times cos(4\theta) \Rightarrow x^2+y^2= x$

3. That looks correct, and no, the variable doesn't really matter.

4. Originally Posted by pickslides
I would take $\displaystyle r = cos(4\theta)$ and multiply both sides by $\displaystyle r$

this gives $\displaystyle r^2= r\times cos(4\theta)$

and using $\displaystyle r^2 = x^2+y^2$

$\displaystyle r^2= r\times cos(4\theta) \Rightarrow x^2+y^2= x$
$\displaystyle r \cos (4 \theta) \neq x$.

Diroga's original solution was perfectly correct and adequate.

As for the $\displaystyle t$, $\displaystyle \theta$ business - if the question asks to have it in terms of $\displaystyle t$ then put it in terms of $\displaystyle t$. This is just a matter of convention.