# What is the distance between the following polar coordinates?: <mstyle displaystyle="true">

Karina Trujillo 2022-06-24 Answered
What is the distance between the following polar coordinates?:
$\left(9,\frac{17\pi }{12}\right),\left(4,\frac{3\pi }{8}\right)$
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Step 1
Plotting these two points, there is a triangle formed whose central angle measures
$3\frac{\pi }{8}+7\frac{\pi }{12}=23\frac{\pi }{24}$
By the Law of Cosines, the distance, c, between the points is found by
${c}^{2}={9}^{2}+{4}^{2}-\left(9\right)\left(4\right)\mathrm{cos}\left(\frac{23\pi }{24}\right)$
That is
${c}^{2}=97-36\mathrm{cos}\left(\frac{23\pi }{24}\right)$
The value of c is the positive square root of the expression on the right side.

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