What is the distance between the following polar coordinates?: (2,(pi)/4), (5,(5pi)/8) (2,π4),(5,5π8)
1 Answer
Apr 16, 2017
Explanation:
If we denote
theta = (5pi)/8- pi/4 = (3pi)/8 θ=5π8−π4=3π8
If we apply the cosine rule:
a^2 = b^2 + c^2 - 2abcosA a2=b2+c2−2abcosA
Then we get:
(AB)^2 = (OA)^2 + (OB)^2 - 2(OA)(OB)costheta (AB)2=(OA)2+(OB)2−2(OA)(OB)cosθ
" " = (2)^2 + (5)^2 - 2(2)(5)cos((3pi)/8) =(2)2+(5)2−2(2)(5)cos(3π8)
" " = 4+25 - 20cos((3pi)/8) =4+25−20cos(3π8)
" " = 29 - 20cos((3pi)/8) =29−20cos(3π8)
" " = 21.34633...
:. AB = 4.629209