# What is the Cartesian form of #(-49,(-3pi)/4)#?

The answer is (Rounded off)

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To convert the polar coordinates ((-49, -\frac{3\pi}{4})) to Cartesian coordinates, we use the following formulas:

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

Given ( r = -49 ) and ( \theta = -\frac{3\pi}{4} ), we substitute these values into the formulas:

[ x = -49 \cos\left(-\frac{3\pi}{4}\right) ] [ y = -49 \sin\left(-\frac{3\pi}{4}\right) ]

Remembering that ( \cos(-\theta) = \cos(\theta) ) and ( \sin(-\theta) = -\sin(\theta) ), we get:

[ x = -49 \cdot \frac{\sqrt{2}}{2} = -49\sqrt{2}/2 ] [ y = -49 \cdot (-\frac{\sqrt{2}}{2}) = 49\sqrt{2}/2 ]

So, the Cartesian coordinates are ((-49\sqrt{2}/2, 49\sqrt{2}/2)).

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