What is the distance between the following polar coordinates?: $(4, π), (5, π)$ $(4,pi), (5,pi)$

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What is the distance between the following polar coordinates?: $(4, π), (5, π)$ $(4,pi), (5,pi)$

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Answer 1 · 2015-12-26T20:23:23

$1$ $1$

Explanation:

The distance formula for polar coordinates is

$d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{1} - θ_{2})}$ $d=sqrt(r_1^2+r_2^2-2r_1r_2Cos(theta_1-theta_2)$
Where $d$ $d$ is the distance between the two points, $r_{1}$ $r_1$ , and $θ_{1}$ $theta_1$ are the polar coordinates of one point and $r_{2}$ $r_2$ and $θ_{2}$ $theta_2$ are the polar coordinates of another point.
Let $(r_{1}, θ_{1})$ $(r_1,theta_1)$ represent $(4, π)$ $(4,pi)$ and $(r_{2}, θ_{2})$ $(r_2,theta_2)$ represent $(5, π)$ $(5,pi)$ .
$\Rightarrow d = \sqrt{4^{2} + 5^{2} - 2 \cdot 4 \cdot 5 cos (π - π)}$ $implies d=sqrt(4^2+5^2-2*4*5Cos(pi-pi)$
$\Rightarrow d = \sqrt{16 + 25 - 40 cos (0)}$ $implies d=sqrt(16+25-40Cos(0)$
$\Rightarrow d = \sqrt{41 - 40 \cdot 1} = \sqrt{41 - 40} = \sqrt{1} = 1$ $implies d=sqrt(41-40*1)=sqrt(41-40)=sqrt(1)=1$
$\Rightarrow d = 1$ $implies d=1$
Hence the distance between the given points is $1$ $1$ .

Answer 2 · 2015-12-29T12:24:36

$1$ $1$

Explanation:

(this is an attempt to restore my original answer)

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Using common insight rather than applying the Pythagorean Theorem and $cos$ $cos$ conversions:

The distance between any two polar coordinates with the same angle is the difference in their radii.

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What is the distance between the following polar coordinates?: $(4, π), (5, π)$ $(4,pi), (5,pi)$

2 Answers

Explanation:

Explanation:

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What is the distance between the following polar coordinates?: (4,π),(5,π) (4,pi), (5,pi)

2 Answers

Explanation:

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What is the distance between the following polar coordinates?: $(4, π), (5, π)$ $(4,pi), (5,pi)$