What is the distance between the following polar coordinates?: # (2,(3pi)/4), (1,(15pi)/8) #
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It is nontrivial to determine polar distances (since drawing a line in polar coordinates isn't very easy), so we should convert to Cartesian coordinates.
This allows us to use Pythagorean theorem in order to find the distance between the two points:
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To find the distance between the polar coordinates ( (2, \frac{3\pi}{4}) ) and ( (1, \frac{15\pi}{8}) ):

Convert each polar coordinate to Cartesian coordinates using the formulas: [ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

For ( (2, \frac{3\pi}{4}) ): [ x_1 = 2 \cos\left(\frac{3\pi}{4}\right) ] [ y_1 = 2 \sin\left(\frac{3\pi}{4}\right) ]

For ( (1, \frac{15\pi}{8}) ): [ x_2 = 1 \cos\left(\frac{15\pi}{8}\right) ] [ y_2 = 1 \sin\left(\frac{15\pi}{8}\right) ]

Calculate the distance between the two Cartesian points using the distance formula: [ d = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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