How do you find the distance between the points with the given polar coordinates $P_1(1.3,-47^circ)$ and $P_2(-3.6, -62^circ)$ ?

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Answer 1 · 2016-11-21T23:13:11

Please see the explanation.

Let's begin by making the radius of $P_2$ positive; we do this by adding $180^@$ to the angle and changing the sign of the radius:

$P_2 = (3.6, 118^@)$

The angle, $theta$ between two line segments drawn from the origin to these two points is:

$theta = 118^@ - -47^@ = 165^@$

Line segment $a = 1.3" units"$
Line segment $b = 3.6" units"$

We can use the Law of Cosines to find the length of line segment c between the two points:

$c = sqrt(a^2 + b^2 - 2(a)(b)cos(theta))$

$c = sqrt(1.3^2 + 3.6^2 - 2(1.3)(3.6)cos(165^@))$

$c ~~ 4.867" units"$

How do you find the distance between the points with the given polar coordinates P_1(1.3,-47^circ)P_1(1.3,-47^circ) and P_2(-3.6, -62^circ)P_2(-3.6, -62^circ)?