What are the components of the vector between the origin and the polar coordinate #(9, (-3pi)/4)#?

1 Answer
Mar 16, 2016

#((-9/2sqrt2),(-9/2sqrt2)) #

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 #