What is the distance between polar coordinates $(- 2, 300^{\circ})$ $(-2, 300^circ)$ and $(2, 10^{\circ})$ $(2, 10^circ)$ ?

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What is the distance between polar coordinates $(- 2, 300^{\circ})$ $(-2, 300^circ)$ and $(2, 10^{\circ})$ $(2, 10^circ)$ ?

1 Answer

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Answer 1 · 2018-07-09T06:23:12

$Distance d \approx 3.2766$ $color(indigo)("Distance " d ~~ 3.2766$

Explanation:

![https://www.aplustopper.com/stewart-calculus-7e-solutions-chapter-10-parametric-equations-polar-coordinates-exercise-10-3/]( useruploads.socratic.org )

$d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{1} - θ_{2})}$ $d = sqrt (r_1^2 + r_2 ^2 - 2 r_1 r_2 cos (theta_1 - theta_2))$

$(r_{1}, θ_{1}) = (- 2, 300^{\circ}), (r_{2}, θ_{2}) = (2, 10^{\circ})$ $(r_1, theta_1) = (-2, 300^@), (r_2, theta_2) = (2, 10^@)$

$d = \sqrt{- 2^{2} + 2^{2} - 2 \cdot - 2 \cdot 2 \cdot cos (300 - 10)}$ $d = sqrt(-2^2 + 2^2 - 2 * -2 * 2 * cos (300-10)$

$d = \sqrt{8 + 8 cos 290} \approx 3.2766$ $d = sqrt (8 + 8 cos 290) ~~ 3.2766$

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What is the distance between polar coordinates $(- 2, 300^{\circ})$ $(-2, 300^circ)$ and $(2, 10^{\circ})$ $(2, 10^circ)$ ?

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What is the distance between polar coordinates $(- 2, 300^{\circ})$ $(-2, 300^circ)$ and $(2, 10^{\circ})$ $(2, 10^circ)$ ?