# What is the distance between the following polar coordinates?: # (3,(15pi)/8), (9,(-2pi)/8) #

Distance is

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The distance between the polar coordinates ( (3, \frac{15\pi}{8}) ) and ( (9, \frac{-2\pi}{8}) ) can be found using the formula:

[ \text{Distance} = \sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos(\theta_2 - \theta_1)} ]

Substituting the given values:

[ r_1 = 3, \ r_2 = 9, \ \theta_1 = \frac{15\pi}{8}, \ \theta_2 = \frac{-2\pi}{8} ]

[ \text{Distance} = \sqrt{3^2 + 9^2 - 2(3)(9)\cos\left(\frac{-2\pi}{8} - \frac{15\pi}{8}\right)} ]

[ \text{Distance} = \sqrt{9 + 81 - 54\cos\left(\frac{-2\pi - 15\pi}{8}\right)} ]

[ \text{Distance} = \sqrt{90 - 54\cos\left(\frac{-17\pi}{8}\right)} ]

Since ( \cos(\frac{-17\pi}{8}) = \cos(\frac{\pi}{8}) ), we can rewrite:

[ \text{Distance} = \sqrt{90 - 54\cos\left(\frac{\pi}{8}\right)} ]

Now, calculate the value of ( \cos\left(\frac{\pi}{8}\right) ) and then substitute it back into the formula to find the distance.

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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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