Question

WILL MARK

14. Find the distance between p1(7, 217/180pi) and p2(5, -23/36pi) ) on the polar plane. (Show work)

Answer 1

Explanation:

The distance

(d) between

P1(7,217/180π)

and P2(5,−23/36π)

on the polar plane is:

d=√72+52−2(7)(5)cos(217/180π+23/36π)

Using the distance formula for polar coordinates

=√49+25−70cos(217+115/180π)

=√74−70cos(332180π)

=√74−70×0.8829

=√74−61.803

=√12.197

=3.49 units

Answer 2

about 3.492

Explanation:

The distance between points in polar coordinates can be found using the Law of Cosines. For vector magnitudes a and b, and angular difference C, the distance between them (c) can be found from ...

c^2 = a^2 +b^2 -2ab·cos(C)

= 7^2 +5^2 -2(7)(5)cos((217/180π -(-23/36)π)

= 74 -70cos(332°) ≈ 12.1937

c = √12.1937 ≈ 3.492

The distance between the given points is about 3.492 units.