Convert the polar coordinate $(3, \frac{5 π}{3})$ to Cartesian coordinates. Enter exact values.
$x =$
$y =$
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Final Answer: $x = \frac{3}{2}$ and $y = - \frac{3 \sqrt{3}}{2}$

Steps

Step 1 ：Use the formulas $x = r \cos (θ)$ and $y = r \sin (θ)$ to convert polar coordinates to Cartesian coordinates

Step 2 ：Given polar coordinate is $(3, \frac{5 π}{3})$ , where $r = 3$ and $θ = \frac{5 π}{3}$

Step 3 ：Calculate $x$ using the formula $x = r \cos (θ)$ : $x = 3 \cos (\frac{5 π}{3})$

Step 4 ：Calculate $y$ using the formula $y = r \sin (θ)$ : $y = 3 \sin (\frac{5 π}{3})$

Step 5 ：Simplify the values of $x$ and $y$

Step 6 ：Final Answer: $x = \frac{3}{2}$ and $y = - \frac{3 \sqrt{3}}{2}$