# What is the Cartesian form of #(12,(5pi )/3)#?

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The Cartesian form of the point ( (12, \frac{5\pi}{3}) ) is obtained by converting from polar coordinates to Cartesian coordinates. To do this, use the following conversions:

[ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

Given the polar coordinates ( (r, \theta) = (12, \frac{5\pi}{3}) ), substitute these values into the formulas to find the Cartesian coordinates:

[ x = 12 \cos\left(\frac{5\pi}{3}\right) ] [ y = 12 \sin\left(\frac{5\pi}{3}\right) ]

Evaluate the trigonometric functions:

[ x = 12 \cos\left(\frac{5\pi}{3}\right) = 12 \cdot \left(-\frac{1}{2}\right) = -6 ] [ y = 12 \sin\left(\frac{5\pi}{3}\right) = 12 \cdot \left(-\frac{\sqrt{3}}{2}\right) = -6\sqrt{3} ]

So, the Cartesian form of ( (12, \frac{5\pi}{3}) ) is ( (-6, -6\sqrt{3}) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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