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

Question

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

stefjumnmt · Accepted Answer

Step 1
The distance formula for polar coordinates is
$d = \sqrt{r_{1}^{2} r_{2}^{2} - 2 r_{1} r_{2} \cos (θ_{1} - θ_{2})}$
Where d is the distance between the two points, $r_{1}$ , and $θ_{1}$ are the polar coordinates of one point and $r_{2}$ and $θ_{2}$ are the polar coordinates of another point.
Let $(r_{1}, θ_{1})$ represent $(4, π)$ and $(r_{2}, θ_{2})$ represent $(5, π)$
$\Rightarrow d = \sqrt{4^{2} + 5^{2} - 2 \times 4 \times 5 \cos (π - π)}$
$\Rightarrow d = \sqrt{16 + 25 - 40 \cos (0)}$
$\Rightarrow d = \sqrt{41 - 40 \times 1} = \sqrt{41 - 40} = \sqrt{1} = 1$
$\Rightarrow d = 1$
Hence the distance between the given points is 1.

Iacopelli5co · Accepted Answer

Step 1    Using common insight rather than applying the Pythagorean Theorem and  cos conversions:  The distance between any two polar coordinates with the same angle is the difference in their radii.

What is the distance between the following polar coordinates?: (4,\

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