数学函数

显示全部楼层 · 2008-8-22 11:02:13

已知sos x-sin x=3√2/5，求：
（1）cos(x+π/4)的值
（2）sin 2x的值
（3）sin^2(x-/π4)的值
要有过程

千问 · 2008-8-22 11:02:13

(1) sinx-cosx=√2(√2/2*sinx-√2/2*cosx) =√2(sinxcosπ/4-cosxsinπ/4) =√2sin(x-π/4)=-3√2/5 sin(x-π/4)=-3/5 cos(x+π/4)=cos[π/2-(x-π/4)]=sin(x-π/4)=-3/5 （2）cos x-sin x=3√2/5 (cosx)^2-2sinxcosx+(sinx)^2=18/25 1-sin2x=18/25 sin2x=7/25 （3）由(1)得sin(x-π/4)=-3/5 所以[sin(x-π/4)]^2=9/25 小朋友要认真学数学。不要老要别人写答案给...

千问 · 2008-8-22 11:02:13

sinx-cosx=√2(√2/2*sinx-√2/2*cosx)=√2(sinxcosπ/4-cosxsinπ/4)=√2sin(x-π/4)=-3√2/5sin(x-π/4)=-3/5cos(x+π/4)=cos[π/2-(x-π/4)]=sin(x-π/4)=-3/5cos x-sin x=3√2/5两边平方(cos...