Question #f6623

1 Answer
Cri007
Mar 12, 2017

#x=frac(pi)(3)+2pin# and #x=-frac(pi)(3)+2pin#

Explanation:

Add #2# to both sides of the equation, and then divide by #4#. We get that #cos(x)=frac(1)(2)#.
On the unit circle, cosine is positive in Quadrants 1 and 4. #cos(x)=frac(1)(2)# when #x=frac(pi)(3)#, or when #x=-frac(pi)(3)#. However, the period of the cosine graph is every #2pi#, so if #n# is our integer constant, then #x=frac(pi)(3)+2pin# and #x=-frac(pi)(3)+2pin#.

If you do not want the "#-frac(pi)(3)#", this is equivalent to #frac(5pi)(3)#.

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