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

1 Answer
Apr 16, 2017

#4.6# to 2dp

Explanation:

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If we denote #(2,pi/4)# by #A#, #(5,(5pi)/8)# by #B# and the origin by #O#, and the angle #angle AOB# by #theta#, Then:

# theta = (5pi)/8- pi/4 = (3pi)/8 #

If we apply the cosine rule:

# a^2 = b^2 + c^2 - 2abcosA #

Then we get:

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

# :. AB = 4.629209 #