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

Leland Morrow 2022-06-15 Answered
What is the distance between the following polar coordinates?:
$\left(3,\frac{17\pi }{12}\right),\left(5,\frac{7\pi }{8}\right)$
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Step 1
$\mathrm{cos}\frac{17\pi }{12}=\mathrm{cos}255=-0.2588\phantom{\rule{0ex}{0ex}}\mathrm{sin}\frac{17\pi }{12}=\mathrm{sin}255=-0.9659$
In cartesean coordinates the first point would be $\left(3\mathrm{cos}17\frac{\pi }{12},3\mathrm{sin}17\frac{\pi }{12}\right)$ Or, (-0.77645, -2.89777)
Second point would be $\left(5\mathrm{cos}7\frac{\pi }{8},5\mathrm{sin}7\frac{\pi }{8}\right)$
Or, (-4.6194, 1.9134)
Apply distance formula to get the distance =6.15549