How do you convert polar equations to Cartesian equation given $theta = pi/3$ ?

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Answer 1 · 2016-11-15T03:36:41

Please see the explanation

$pi/3$ is in the first quadrant, therefore, we substitute $tan^-1(y/x)$ for $theta$ and add the restriction $x > 0 and y > 0$ :

$tan^-1(y/x) = pi/3; x > 0 and y > 0$

Use the tangent function on both sides:

$tan(tan^-1(y/x)) = tan(pi/3); x > 0 and y > 0$

The tangent function "undoes" its inverse and $tan(pi/3)$ has a well known value:

$y/x = sqrt(3); x > 0 and y > 0$

Multiply both sides by x and drop the restriction on y, because it is now dependent on x:

$y = sqrt(3)x; x > 0$

How do you convert polar equations to Cartesian equation given theta = pi/3theta = pi/3?