"What is the distance between the following polar..." was answered by our community

dohtarjev510

Answered question

2022-02-02

What is the distance between the following polar coordinates?:

(5, \frac{- 5 π}{12}), (5, \frac{11 π}{6})

laiedkn

Beginner2022-02-03Added 15 answers

Given:

r_{1} = 5

θ_{1} = - \frac{5 π}{12}

r_{2} = 5

θ_{2} = \frac{11 π}{6}

The distance formula for polar coordinates is

D = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} \cos (θ_{1} - θ_{2})}

D = \sqrt{5^{2} + 5^{2} - 2 (5) (5) \cos (- \frac{5 π}{12} - \frac{11 π}{6})}

= \sqrt{25 + 25 - 50 \cos (- \frac{9 π}{4})}

D = \sqrt{50 + 50 \frac{\sqrt{2}}{2}} \approx 9.2388

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