boloman0z

2022-06-25

What is the distance between the following polar coordinates?: $\left(7,\frac{5\pi }{4}\right),\left(1,\frac{15\pi }{8}\right)$

enfujahl

Expert

Step 1
$d=\sqrt{{r}_{1}^{2}-2{r}_{1}{r}_{2}\mathrm{cos}\left({\theta }_{1}-{\theta }_{2}\right)+{r}_{2}^{2}}$
Step 2
$d=\sqrt{{7}^{2}-2\left(7\right)\left(1\right)\mathrm{cos}\left(\frac{5\pi }{4}-\frac{15\pi }{8}\right)+{1}^{2}}$
Answer: $d\approx 7.44$

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