What is the distance between the following polar coordinates?: (2,(pi)/4), (5,(5pi)/8) (2,π4),(5,5π8)

1 Answer
Apr 16, 2017

4.64.6 to 2dp

Explanation:

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If we denote (2,pi/4)(2,π4) by AA, (5,(5pi)/8)(5,5π8) by BB and the origin by OO, and the angle angle AOBAOB by thetaθ, Then:

theta = (5pi)/8- pi/4 = (3pi)/8 θ=5π8π4=3π8

If we apply the cosine rule:

a^2 = b^2 + c^2 - 2abcosA a2=b2+c22abcosA

Then we get:

(AB)^2 = (OA)^2 + (OB)^2 - 2(OA)(OB)costheta (AB)2=(OA)2+(OB)22(OA)(OB)cosθ
" " = (2)^2 + (5)^2 - 2(2)(5)cos((3pi)/8) =(2)2+(5)22(2)(5)cos(3π8)
" " = 4+25 - 20cos((3pi)/8) =4+2520cos(3π8)
" " = 29 - 20cos((3pi)/8) =2920cos(3π8)
" " = 21.34633...

:. AB = 4.629209