How do you convert polar equations to Cartesian equation given $θ = \frac{π}{3}$ $theta = pi/3$ ?

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How do you convert polar equations to Cartesian equation given $θ = \frac{π}{3}$ $theta = pi/3$ ?

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Answer 1 · 2016-11-15T03:36:41

Please see the explanation

Explanation:

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

${tan}^{- 1} (\frac{y}{x}) = \frac{π}{3}; x > 0 and y > 0$ $tan^-1(y/x) = pi/3; x > 0 and y > 0$

Use the tangent function on both sides:

$tan ({tan}^{- 1} (\frac{y}{x})) = tan (\frac{π}{3}); x > 0 and y > 0$ $tan(tan^-1(y/x)) = tan(pi/3); x > 0 and y > 0$

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

$\frac{y}{x} = \sqrt{3}; x > 0 and y > 0$ $y/x = sqrt(3); x > 0 and y > 0$

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

$y = \sqrt{3} x; x > 0$ $y = sqrt(3)x; x > 0$

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How do you convert polar equations to Cartesian equation given $θ = \frac{π}{3}$ $theta = pi/3$ ?

1 Answer

Explanation:

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How do you convert polar equations to Cartesian equation given theta = pi/3θ=π3theta = pi/3?

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How do you convert polar equations to Cartesian equation given $θ = \frac{π}{3}$ $theta = pi/3$ ?