Problem

Find polar coordinates of the point that has rectangular coordinates $(-3 \sqrt{3}, 3)$. Write your answer using degrees.

Answer

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Answer

Final Answer: \(\boxed{(6, 150^\circ)}\)

Steps

Step 1 :The rectangular coordinates of the point are given as $(-3 \sqrt{3}, 3)$.

Step 2 :We can find the polar coordinates $(r, \theta)$ of this point using the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \arctan(\frac{y}{x})$.

Step 3 :Substituting the given values into the formula for $r$, we get $r = \sqrt{(-3 \sqrt{3})^2 + 3^2} = 6$.

Step 4 :Substituting the given values into the formula for $\theta$, we get $\theta = \arctan(\frac{3}{-3 \sqrt{3}})$. However, since the point is in the second quadrant, we need to add 180 degrees to the result of the arctangent function, giving us $\theta = 150$ degrees.

Step 5 :Therefore, the polar coordinates of the point $(-3 \sqrt{3}, 3)$ are $(6, 150^\circ)$.

Step 6 :Final Answer: \(\boxed{(6, 150^\circ)}\)

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