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Question

# Convert the polar coordinates to Cartesian coordinates. Give exact answers. $( 1,2 \pi / 3 )$

Solution

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Given to us is the polar coordinates $(r , \theta)$ given by Point $( 1,2 \pi / 3 )$. The angle $\theta$ is $\dfrac{2\pi}{3}$ .The cartesian coordinates of Points are

$\textbf{x -coordinate}$

\begin{align*} x &= r \cos \theta \\ x &= 1 \cos 2 \pi / 3 \\ x &= \frac { - 1 } { 2 } \end{align*}

$\textbf{y -coordinate}$

\begin{align*} y & = r \sin \theta \\ y & = 1 \sin 2 \pi / 3 \\ y & = \frac { \sqrt { 3 } } { 2 } \end{align*}

Hence cartesian Coordinates are $\left( \dfrac { - 1 } { 2 } , \dfrac { \sqrt { 3 } } { 2 } \right)$

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