f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下:f(x)=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间:π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4
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![f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下:f(x)=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间:π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4](/uploads/image/z/12051961-25-1.jpg?t=f%28x%29%3Dsin+x+%28sinx-cosx%29%E7%9A%84%E5%87%8F%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%3Ff%28x%29%3Dsin+x+%28sinx-cosx%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%E8%A7%A3%E5%A6%82%E4%B8%8B%EF%BC%9Af%EF%BC%88x%EF%BC%89%3Dsin%5E2+X+-+sinxcosx%3D2sinxcosx-sinxcox%3Dsinxcox%3D1%2F2sin+2xsinx%E7%9A%84%E5%8D%95%E8%B0%83%E5%87%8F%E5%8C%BA%E9%97%B4%EF%BC%9A%CF%80%2F2%2B2k%CF%80+%3C+x+%3C+3%CF%80%2F2%2B2k%CF%80%CF%80%2F2%2B2k%CF%80+%3C+2x+%3C+3%CF%80%2F2%2B2k%CF%80%CF%80%2F4%2Bk%CF%80%3C+X+%3C+3%CF%80%2F4)
f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下:f(x)=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间:π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4
f(x)=sin x (sinx-cosx)的减单调区间?
f(x)=sin x (sinx-cosx)的单调区间
解如下:
f(x)=sin^2 X - sinxcosx
=2sinxcosx-sinxcox
=sinxcox
=1/2sin 2x
sinx的单调减区间:π/2+2kπ < x < 3π/2+2kπ
π/2+2kπ < 2x < 3π/2+2kπ
π/4+kπ< X < 3π/4+kπ
[ kπ-3/8π ,kπ-π/8 ]
请问我哪里算错了?
f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下:f(x)=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间:π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4
f(x)=sin^2 X - sinxcosx
=2sinxcosx-sinxcox错
=(cos2x+1)/2-sinxcox
=1/2cos2x-1/2sin2x+1/2
=√2/2sin(π/4-2x)+1/2
单调减区间:
π/2+2kπ < π/4-2x< 3π/2+2kπ
-5π/8+kπ < x< -π/8+kπ
单调递增区间
-π/2+2kπ < π/4-2x< π/2+2kπ
-π/8+kπ < x < 3π/8+kπ
sin^2 X=2sinxcosx错了
应为(1-COS2X)/2