What are the components of the vector between the origin and the polar coordinate #(6, (3pi)/4)#?
1 Answer
Feb 12, 2016
# ((-3sqrt2),(3sqrt2))#
Explanation:
using the formulae that links Polar to Cartesian coordinates.
#• x = rcostheta #
#• y = rsintheta # in this question: r = 6 and
# theta = (3pi)/4 #
# rArr x = 6cos((3pi)/4) = 6.(- 1/sqrt2) = -3sqrt2 # [note :
# 1/sqrt2 = sqrt2/(sqrt2 .sqrt2) = 1/2 sqrt2] # and using exact values for
# cos((3pi)/4)color(black)(" and ") sin((3pi)/4)#
# rArr y = 6sin((3pi)/4) = 6.(1/sqrt2) = 3sqrt2 #
