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Convert $$$\left(\rho, \theta\right) = \left(20, \frac{11 \pi}{6}\right)$$$ to rectangular coordinates

For the point $$$\left(\rho, \theta\right) = \left(20, \frac{11 \pi}{6}\right)$$$ given in polar coordinates, the calculator will find its rectangular (Cartesian) coordinates, with steps shown.

Related calculator: Polar/Rectangular Equation Calculator

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Your Input

Convert $$$\left(\rho, \theta\right) = \left(20, \frac{11 \pi}{6}\right)$$$ to rectangular coordinates.

Solution

Conversion from polar coordinates to rectangular coordinates is simple: $$$x = \rho \cos{\left(\theta \right)}$$$, $$$x = \rho \sin{\left(\theta \right)}$$$.

So, $$$x = 20 \cos{\left(\frac{11 \pi}{6} \right)} = 10 \sqrt{3}$$$ and $$$y = 20 \sin{\left(\frac{11 \pi}{6} \right)} = -10$$$.

Answer

$$$\left(x, y\right) = \left(10 \sqrt{3}, -10\right)\approx \left(17.320508075688773, -10\right)$$$A