# What is the distance between the following polar coordinates?: # (1,(5pi)/4), (5,(3pi)/8) #

5.93577 approx

Or(1.9134, 4.6194)

Use distance formula to get it=5.93577 approx

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To find the distance between two polar coordinates, you can use the formula:

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

Given the coordinates: ( r_1 = 1 ), ( \theta_1 = \frac{5\pi}{4} ) ( r_2 = 5 ), ( \theta_2 = \frac{3\pi}{8} )

Substitute the values into the formula:

[ \text{distance} = \sqrt{1^2 + 5^2 - 2 \cdot 1 \cdot 5 \cdot \cos\left(\frac{3\pi}{8} - \frac{5\pi}{4}\right)} ]

[ \text{distance} = \sqrt{1 + 25 - 10\cos\left(\frac{3\pi}{8} - \frac{5\pi}{4}\right)} ]

[ \text{distance} = \sqrt{26 - 10\cos\left(\frac{3\pi}{8} - \frac{5\pi}{4}\right)} ]

[ \text{distance} = \sqrt{26 - 10\cos\left(\frac{3\pi}{8} - \frac{10\pi}{8}\right)} ]

[ \text{distance} = \sqrt{26 - 10\cos\left(-\frac{7\pi}{8}\right)} ]

[ \text{distance} = \sqrt{26 - 10\cos\left(\frac{7\pi}{8}\right)} ]

[ \text{distance} = \sqrt{26 - 10\left(-\frac{\sqrt{2}}{2}\right)} ]

[ \text{distance} = \sqrt{26 + 5\sqrt{2}} ]

Therefore, the distance between the polar coordinates is ( \sqrt{26 + 5\sqrt{2}} ).

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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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