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

What is the distance between the following polar coordinates?:
$\left(5,\frac{5\pi }{4}\right),\left(2,\frac{11\pi }{8}\right)$
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Step 1
If $A\left(5,\frac{5\pi }{4}\right)$, $Β\left(2,\frac{11\pi }{8}\right)$
${d}_{AB}=\sqrt{{x}_{1}^{2}+{x}_{2}^{2}-2{x}_{1}{x}_{2}\mathrm{cos}\left({\theta }_{1}-{\theta }_{2}\right)}$
Step 2
$\sqrt{{5}^{2}+{2}^{2}-2\cdot 5\cdot 2\mathrm{cos}\left(\frac{5\pi }{4}-\frac{11\pi }{8}\right)}$
$\sqrt{25+4-20\mathrm{cos}\left(-\frac{\pi }{8}\right)}$
$\sqrt{29-20\mathrm{cos}\left(\frac{\pi }{8}\right)}$
$\sqrt{29-20\frac{\sqrt{2+\sqrt{2}}}{2}}$
$\sqrt{29-10\sqrt{2+\sqrt{2}}}$