Show that in a polar coordinate system the distance d betweenthe points (r1, 1) and (r2

Chapter 10, Problem 71

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Show that in a polar coordinate system the distance $d$ between the points $\left(r_{1}, \theta_{1}\right)$ and $\left(r_{2}, \theta_{2}\right)$ is

$d=\sqrt{r_{1}^{2}+r_{2}^{2}-2 r_{1} r_{2} \cos \left(\theta_{1}-\theta_{2}\right)}$

Equation Transcription:

$d$

$({r}_{1},{\theta{}}_{1})$

$({r}_{2},{\theta{}}_{2})$

$d=\sqrt{{r}_{1}^{2}+{r}_{2}^{2}-2{r}_{1}{r}_{2}cos({\theta{}}_{1}-{\theta{}}_{2})}$

Text Transcription:

(r_1,theta_1)

(r_2,theta_2)

d=r_1^2+r_2^2-2r_1 r_2 cos(theta_1-_theta2)

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