Question: "What is the distance between the following polar..."

Ella Moon

Answered question

2022-02-02

What is the distance between the following polar coordinates?:

(3, \frac{7 π}{12}), (1, \frac{17 π}{8})

Emilie Mcpherson

Beginner2022-02-03Added 12 answers

The distance formula for rectangular coordinates is

D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

Plugging in

x_{n} = r_{n} \cos (θ_{n}) and y_{n} = r_{n} \sin (θ_{n})

, expanding, and simplifying gives

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

Plugging in

(r_{1}, θ_{1}) = (3, \frac{7 π}{12}) and (r_{2}, θ_{2}) = (1, \frac{17 π}{8})

D = \sqrt{3^{2} + 1^{1} - 2 (3) (1) \cos (\frac{17 π}{8} - \frac{7 π}{12})}

D = \sqrt{10 - 6 \cos (\frac{37 π}{24})}

D \approx 3.04

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