# What is the distance between the following polar coordinates?: # (5,(17pi)/12), (9,(11pi)/8) #

Polar coordinates of point A is:

Polar coordinates of point B is:

Distance between points A and B can be found using:

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To find the distance between two polar coordinates ((r_1, \theta_1)) and ((r_2, \theta_2)), you can use the formula:

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

Substitute the given values:

[ r_1 = 5, \theta_1 = \frac{17\pi}{12}, r_2 = 9, \theta_2 = \frac{11\pi}{8} ]

[ d = \sqrt{5^2 + 9^2 - 2(5)(9)\cos\left(\frac{11\pi}{8} - \frac{17\pi}{12}\right)} ]

[ d = \sqrt{25 + 81 - 90\cos\left(\frac{11\pi}{8} - \frac{17\pi}{12}\right)} ]

[ d = \sqrt{106 - 90\cos\left(\frac{11\pi}{8} - \frac{17\pi}{12}\right)} ]

Now, calculate the difference of the angles:

[ \frac{11\pi}{8} - \frac{17\pi}{12} = \frac{33\pi}{24} - \frac{34\pi}{24} = -\frac{\pi}{24} ]

[ d = \sqrt{106 - 90\cos\left(-\frac{\pi}{24}\right)} ]

[ d = \sqrt{106 - 90\cos\left(\frac{\pi}{24}\right)} ]

[ d \approx \sqrt{106 - 90 \times 0.9659} ]

[ d \approx \sqrt{106 - 86.931} ]

[ d \approx \sqrt{19.069} ]

[ d \approx 4.366 ]

Therefore, the distance between the given polar coordinates is approximately (4.366).

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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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