函数y=sin^6(x)+cos^6(x)的最小正周期是____
函数y=sin^6(x)+cos^6(x)的最小正周期是π/2。
详解:sin^6(x)+cos^6(x)=[sin^2(x)]^3+[cos^2(x)}^3=
=[sin^2(x)+cos^2(x)}*[sin^4(x)]+[cos^4(x)-sin^2(x)cos^2}=
=1*[sin^4(x)]^3+[cos^4(x)-sin^2(x)cos^2}=
=[sin^2(x)]^+cos^^2(x)]^2-3sin^2(x)cos^2}=
=1-3sin^2(x)cos^2}
=1-3/4(sin2x)^2
=1-(3/4)*(1-cos4x)/2
∴最小正周期是T=2π/4=π/...全部
函数y=sin^6(x)+cos^6(x)的最小正周期是π/2。
详解:sin^6(x)+cos^6(x)=[sin^2(x)]^3+[cos^2(x)}^3=
=[sin^2(x)+cos^2(x)}*[sin^4(x)]+[cos^4(x)-sin^2(x)cos^2}=
=1*[sin^4(x)]^3+[cos^4(x)-sin^2(x)cos^2}=
=[sin^2(x)]^+cos^^2(x)]^2-3sin^2(x)cos^2}=
=1-3sin^2(x)cos^2}
=1-3/4(sin2x)^2
=1-(3/4)*(1-cos4x)/2
∴最小正周期是T=2π/4=π/2
。收起
