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(y/x) in Q1#

when #(x, y) in Q1 or Q3 #.

Likewise,

the principal value from the calculator for

#arc tan (y/x) in Q2#, when #(x, y) in Q2 or Q4#

Test with #(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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