## Trigonometry (11th Edition) Clone

$d = \sqrt{r_1^2+r_2^2-2~r_1~r_2~cos~(\theta_1-\theta_2)}$
$x_1 = r_1~cos~\theta_1$ $y_1 = r_1~sin~\theta_1$ $x_2 = r_2~cos~\theta_2$ $y_2 = r_2~sin~\theta_2$ We can find the distance between the two points: $d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ $d = \sqrt{(r_1~cos~\theta_1-r_2~cos~\theta_2)^2+(r_1~sin~\theta_1-r_2~sin~\theta_2)^2}$ $d = \sqrt{r_1^2~cos^2~\theta_1+r_2^2~cos^2~\theta_2-2~r_1~r_2~cos~\theta_1~cos~\theta_2+r_1^2~sin^2~\theta_1+r_2^2~sin^2~\theta_2-2~r_1~r_2~sin~\theta_1~sin~\theta_2}$ $d = \sqrt{r_1^2~(cos^2~\theta_1+sin^2~\theta_1)+r_2^2~(cos^2~\theta_2+sin^2~\theta_2)-2~r_1~r_2~cos~\theta_1~cos~\theta_2-2~r_1~r_2~sin~\theta_1~sin~\theta_2}$ $d = \sqrt{r_1^2~(1)+r_2^2~(1)-2~r_1~r_2~(cos~\theta_1~cos~\theta_2+sin~\theta_1~sin~\theta_2)}$ $d = \sqrt{r_1^2+r_2^2-2~r_1~r_2~cos~(\theta_1-\theta_2)}$