What are the components of the vector between the origin and the polar coordinate #(21, (-pi)/8)#?

1 Answer
Andrea S.
Nov 24, 2016

#x = rho cos theta#
#y = rho sin theta#

Explanation:

#x = 21 cos (pi/8)#
#y=-21 sin(pi/8)#

#pi/8# is not an angle for which the value is universally known but you can find it with the trigonometric formula for the bisected angle:

#cos(pi/8) = cos (1/2*pi/4) = sqrt(((1+cos(pi/4))/2))= sqrt(((1+sqrt(2))/2)#
#sin(pi/8) = sin (1/2*pi/4) = sqrt(((1-cos(pi/4))/2))= sqrt(((1-sqrt(2))/2)#

and eventually:

#x = 21 sqrt(((1+sqrt(2))/2)#
#y=-21sqrt(((1-sqrt(2))/2)#

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