Question #9cc39

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What is the formula for converting polar coordinates to rectangular coordinates?
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How do I convert polar coordinates $(6, 60^{\circ})$ $(6, 60^circ)$ to rectangular coordinates?
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What is the Cartesian equivalent of polar coordinates $(\sqrt{97}, 66^{\circ})$ $(sqrt97, 66^circ)$ ?
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What is the Cartesian equivalent of polar coordinates $(7, π)$ $(7, pi)$ ?

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Answer 1 · 2017-11-18T00:16:44

$x^{2} + y^{2} = \frac{6}{4} x + 7 y$ $x^2+y^2 = 6/4x+7y$

You will need to know these subsitutions:

$r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$
$cos (θ) = \frac{x}{r}$ $cos(theta) = x/r$
$sin (θ) = \frac{y}{r}$ $sin(theta) = y/r$

Follow along these steps:

$r = \frac{6}{4} cos θ + 7 sin θ$ $r = 6/4costheta+7sintheta$

Substitute $cos θ$ $costheta$ and $sin θ$ $sintheta$ with their appropriate substitutions.

$r = \frac{6}{4} \cdot \frac{x}{r} + 7 \cdot \frac{y}{r}$ $r = 6/4*x/r+7*y/r$

Multiply both sides by $r$ $r$

$r^{2} = \frac{6}{4} x + 7 y$ $r^2 = 6/4x+7y$

Substitute $r^{2}$ $r^2$ with it's appropriate substitution

$x^{2} + y^{2} = \frac{6}{4} x + 7 y$ $x^2+y^2 = 6/4x+7y$

This is a valid rectangular equation.