Question #07ebb

Question

What is the formula for the distance between two polar coordinates?
How do I find the distance between polar coordinates $(2, 50^circ)$ and $(5, -50^circ)$ ?
How do I find the distance between polar coordinates $(3, 60^circ)$ and $(5, 145^circ)$ ?
How do I find the distance between the points with polar coordinates $(3, 120^circ)$ and #(0.5,...
How do I find the distance between the points with polar coordinates $(2, 120^circ)$ and $(1, 45^circ)$ ?
How do I find the distance between the points with polar coordinates $(2, 10^circ)$ and $(7, 10^circ)$ ?
What is the distance between polar coordinates $(2, 120^circ)$ and $(1, 150^circ)$ ?
What is the distance between polar coordinates $(-4, -30^circ)$ and $(3, 250^circ)$ ?
What is the distance between polar coordinates $(7, -150^circ)$ and $(4, 130^circ)$ ?
What is the distance between polar coordinates $(-2, 300^circ)$ and $(2, 10^circ)$ ?

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Answer 1 · 2016-08-13T04:47:41

Invalid as a general formula..

The principal value from the calculator for $arctan (\frac{y}{x}) \in Q 1$ $arctan(y/x) in Q1$

when $(x, y) \in Q 1 or Q 3$ $(x, y) in Q1 or Q3$ .

Likewise,

the principal value from the calculator for

$a r c tan (\frac{y}{x}) \in Q 2$ $arc tan (y/x) in Q2$ , when $(x, y) \in Q 2 or Q 4$ $(x, y) in Q2 or Q4$

Test with $(x, y) = (\pm 1, \pm 1)$ $(x, y)=(+-1, +-1)$

Any formula equivalent to the couple

$'cos theta = x/r and sin theta = y/r'$ , for fixing $theta$ , is valid.

As sine and cosine are periodic with period $2pi$ , $theta$ identified

in $[0, 2pi]$ would fix the quadrant correctly.
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