# What is the distance between the following polar coordinates?: # (5,(7pi)/4), (3,(9pi)/8) #

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To find the distance between the polar coordinates (5, (7π)/4) and (3, (9π)/8), you can use the distance formula in polar coordinates, which is given by:

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

Plugging in the values, the distance between the two points is:

[ \sqrt{5^2 + 3^2 - 2(5)(3)\cos\left(\frac{9\pi}{8} - \frac{7\pi}{4}\right)} ]

[ = \sqrt{25 + 9 - 30\cos\left(\frac{9\pi}{8} - \frac{7\pi}{4}\right)} ]

[ = \sqrt{34 - 30\cos\left(\frac{9\pi}{8} - \frac{7\pi}{4}\right)} ]

[ = \sqrt{34 - 30\cos\left(\frac{\pi}{8}\right)} ]

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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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- What is the distance between the following polar coordinates?: # (4,(-8pi)/3), (-5,(11pi)/6) #
- What is the polar form of #( -4,27 )#?

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