Express the polar coordinates $\left(2,-\frac{\pi}{3}\right)$ in Cartesian coordinates.
What is the point in rectangular coordinates?
(Type an ordered pair. Type exact answers for each coordinate, using radicals as needed.)

Answer

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Answer

Final Answer: The Cartesian coordinates of the point are $\boxed{(1, -\sqrt{3})}$

Steps

Step 1 ：Given the polar coordinates $(2,-\frac{\pi}{3})$

Step 2 ：We can convert these to Cartesian coordinates using the formulas $x = r\cos(\theta)$ and $y = r\sin(\theta)$

Step 3 ：Substitute $r = 2$ and $\theta = -\frac{\pi}{3}$ into the formulas

Step 4 ：For x-coordinate, calculate $x = 2\cos(-\frac{\pi}{3}) = 1$

Step 5 ：For y-coordinate, calculate $y = 2\sin(-\frac{\pi}{3}) = -\sqrt{3}$

Step 6 ：Final Answer: The Cartesian coordinates of the point are $\boxed{(1, -\sqrt{3})}$