y=cosx(cosx+sinx)的周期T 求详解

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y=cosx(cosx+sinx)的周期T求详解y=cosx(cosx+sinx)的周期T求详解y=cosx(cosx+sinx)的周期T求详解y=cos²x+sinxcosx=(1+cos

y=cosx(cosx+sinx)的周期T 求详解
y=cosx(cosx+sinx)的周期T 求详解

y=cosx(cosx+sinx)的周期T 求详解
y=cos²x+sinxcosx
=(1+cos2x)/2+1/2*sin2x
=(1/2)(sin2x+cos2x)+1/2
=(√2/2)(√2/2*sin2x+√2/2cos2x)+1/2
=(√2/2)(sin2xcosπ/4+cos2xsinπ/4)+1/2
=(√2/2)sin(2x+π/4)+1/2
故,T=2π/2=π