What are the components of the vector between the origin and the polar coordinate #(9, (-3pi)/4)#?
1 Answer
Mar 16, 2016
Explanation:
Using the formulae that link Polar to Cartesian coordinates.
#• x = rcostheta #
#• y = rsintheta # here r = 9 and
# theta = -(3pi)/4 # hence
# x = 9cos(-(3pi)/4) " and " y = 9sin(-(3pi)/4)#
#"----------------------------------------------------------------------"# now
# cos(-(3pi)/4) = -cos(pi/4)# and
# sin(-(3pi)/4) = -sin(pi/4) # The 'exact' value of
# sin(pi/4) = cos(pi/4) = 1/sqrt2 #
#"-------------------------------------------------------------------------"# thus
# x = -9cos(pi/4) = -9xx1/sqrt2 = -9/2 sqrt2 # and y
# -9sin(pi/4) = -9xx1/sqrt2 = -9/2 sqrt2 #
