gaiaecologicaq2

2022-07-09

What is the distance between the following polar coordinates?:
$\left(5,\frac{17\pi }{12}\right),\left(9,\frac{11\pi }{8}\right)$

Perman7z

Expert

Step 1
Polar coordinates of point A is:
${r}_{1}=5$ and ${\theta }_{1}=\frac{17\pi }{12}$
Polar coordinates of point B is:
${r}_{2}=9$ and ${\theta }_{2}=\frac{11\pi }{8}$
Distance between points A and B can be found using:
$D=\sqrt{{r}_{1}^{2}+{r}_{2}^{2}-2{r}_{1}{r}_{2}\mathrm{cos}\left({\theta }_{1}-{\theta }_{2}\right)}$
$D=\sqrt{{5}^{2}+{9}^{2}-2\cdot 5\cdot 9\mathrm{cos}\left(\left(\frac{17\pi }{12}\right)-\left(\frac{11\pi }{8}\right)\right)}$
$D\approx 4.095$ units

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