How do you convert $r=47/(3sinθ+7cosθ)$ into cartesian form?

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Answer 1 · 2015-11-27T19:01:44

$3y+7x=47$

Divide both sides by $r$ :

$1 = 47/(3rsin(theta)+7rcos(theta))$

You have that

$x=rcos(theta)$
$y=rsin(theta)$ .

Plug all these three into the equation and get

$1=47/(3y+7x)$

which you can write as

$3y+7x=47$

How do you convert r=47/(3sinθ+7cosθ)r=47/(3sinθ+7cosθ) into cartesian form?