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dinsdag 2 mei 2017

De gulden snede

f(x)=sin(x)(sin(x)+2cos(x))f(x)=sin2(x)+2sin(x)cos(x)f(x)=2sin(x)cos(x)+4cos2(x)2f(x)=4cos2(x)+2sin(x)cos(x)2f(x)=0}4cos2(x)+2sin(x)cos(x)2=02cos(2x)+2+sin(2x)2=02cos(2x)+sin(2x)=02+tan(2x)=0tan(2x)=2x=38π12arctan(13)f(38π12arctan(13))=12+125=φ