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How do you find the general solutions for #2cosx - sqrt3 = 0#?

1 Answer

Oct 23, 2015

#x=2npi +-pi/6, AA n in ZZ#

Explanation:

#2cos(x)-sqrt(3)=0#

#rArrcolor(white)("XXX")cos(x) = sqrt(3)/2#

This is a standard trigonometric ratio for a #pi/6# reference angle.

Within the interval #(-pi,+pi]#
#color(white)("XXX")x = +pi/6 or x=-pi/6#

For all solutions it is necessary to include all possoble full circle increments:
#color(white)("XXX")x=2npi+-pi/6, AAn in ZZ#

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