Find all solutions in the interval [0,2pi) of the equation: 2cos(4x)-1=0

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amandasan98 amandasan98

11-03-2017
Mathematics

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Find all solutions in the interval [0,2pi) of the equation: 2cos(4x)-1=0

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jdoe0001 jdoe0001 · Answer 1 · 2017-03-11T22:14:32+01:00

[tex]\bf 2cos(4x)-1=0\implies 2cos(4x)=1\implies cos(4x)=\cfrac{1}{2} \\\\\\ cos^{-1}\left[ cos(4x) \right]=cos^{-1}\left[ \cfrac{1}{2} \right]\implies 4x=cos^{-1}\left( \cfrac{1}{2} \right) \\\\\\ \measuredangle x = \cfrac{cos^{-1}\left( \frac{1}{2} \right)}{4}[/tex]

check your Unit Circle for all angles on that range that have a cosine of 1/2
then divide that by 4... for example hmmmm say [tex]\bf \frac{\pi }{3}[/tex] is one, thus x = [tex]\bf \cfrac{\frac{\pi }{3}}{4}\implies \cfrac{\pi }{3}\cdot \cfrac{1}{4}\implies \cfrac{\pi }{12}[/tex]

that's one