How do you convert #rcos(x/2) - rsin(x/2) = 0# to rectangular form?

1 Answer
Alan P.
Dec 22, 2016

#color(green)(x=0)#

Explanation:

I have assumed that the given equation could be better expressed as
#color(white)("XXX")r cos(theta/2)-r sin(theta/2)=0#
to avoid using #x# which is normally associated with the rectangular form.

#rArr##color(white)("XXX")cancel(r) cos(theta/2)=cancel(r) sin(theta/2)#

#rArr##color(white)("XXX")theta/2 = pi/4 (color(gray)(+-kpi, k in ZZ))#

#rArr##color(white)("XXX")theta = pi/2 (color(gray)(+-k2pi, k in ZZ))#

Therefore we have a vertical line through the origin,
or, in terms of rectangular elements, #x=0#

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