What is the Cartesian form of #( -9, (-7pi)/3 ) #?
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The Cartesian form of the point ((-9, -\frac{7\pi}{3})) is obtained by converting from polar coordinates to Cartesian coordinates.
To convert from polar coordinates ((r, \theta)) to Cartesian coordinates ((x, y)), we use the formulas: [x = r \cos(\theta)] [y = r \sin(\theta)]
Given (r = -9) and (\theta = -\frac{7\pi}{3}), we can calculate (x) and (y): [x = -9 \cos\left(-\frac{7\pi}{3}\right)] [y = -9 \sin\left(-\frac{7\pi}{3}\right)]
Since (\cos\left(-\frac{7\pi}{3}\right) = \cos\left(\frac{5\pi}{3}\right) = \frac{1}{2}) and (\sin\left(-\frac{7\pi}{3}\right) = \sin\left(\frac{5\pi}{3}\right) = -\frac{\sqrt{3}}{2}), we have: [x = -9 \cdot \frac{1}{2} = -\frac{9}{2}] [y = -9 \cdot \left(-\frac{\sqrt{3}}{2}\right) = \frac{9\sqrt{3}}{2}]
Therefore, the Cartesian form of the point ((-9, -\frac{7\pi}{3})) is ((-9/2, 9\sqrt{3}/2)).
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The Cartesian form of (-9, (-7π)/3) is (-9cos((-7π)/3), -9sin((-7π)/3)), which simplifies to (4.5, -7.794).
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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.
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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