How do you convert $r = 8 (cos (x) + (sin (x))$ $r= 8(cos(x)+(sin(x))$ into cartesian form?

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Answer 1 · 2015-11-27T19:00:09

$x^{2} + y^{2} = 8 (x + y)$ $x^2+y^2 = 8(x+y)$

Multiply both sides by $r$ $r$ :

$r^{2} = 8 (r cos (x) + r sin (x))$ $r^2 = 8(rcos(x)+rsin(x))$

Since $r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$ , then $r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$ . On the other hand, you have that

$x = r cos (x)$ $x=rcos(x)$
$y = r sin (x)$ $y=rsin(x)$ .

Plug all these three into the equation and get

$x^{2} + y^{2} = 8 (x + y)$ $x^2+y^2 = 8(x+y)$

How do you convert r= 8(cos(x)+(sin(x))r=8(cos(x)+(sin(x))r= 8(cos(x)+(sin(x)) into cartesian form?