Sin(2x+pi/6)=1/2? Solve using multiple angles?

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Answer 1 · 2018-02-21T20:07:39

#color(blue)(x=pik)#

#color(blue)(x=pi/3+pik)#

#sin(2x+pi/6)=1/2#

#2x+pi/6=arcsin(sin(2x+pi/6)=arcsin(1/2)=> pi/6+2pik, (5pi)/6+2pik#

#2x+pi/6=pi/6+2pik#

#2x=-pi/6+pi/6+2pik#

#color(blue)(x=pik)#

#2x+pi/6=(5pi)/6+2pik#

#2x=-pi/6+(5pi)/6+2pik#

#2x=(2pi)/3+2pik#

#color(blue)(x=pi/3+pik)#

For any integer #bbk#