(1)f(COSX)=COS17x 求证F(SINX)=17X
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/26 19:34:21
(1)f(COSX)=COS17x 求证F(SINX)=17X
(2)已知X属于R,N属于Z且F(SINX)=SIN(4N+1)求F(COSX)
(2)已知X属于R,N属于Z且F(SINX)=SIN(4N+1)求F(COSX)
(1)sinx=cos(π/2-x)
所以f(sinx)=f[cos(π/2-x)]=cos[17(π/2-x)]
=cos(17π/2-17x)
=cos(π/2-17x)
=sin17x
(2)f(cosx)
=f[sin(π/2-x)]
=sin(4n+1)(π/2-x)
=sin[(4n+1)π/2-(4n+1)x]
=sin[2nπ+π/2-(4n+1)x]
=sin[π/2-(4n+1)x]
=cos(4n+1)x
所以f(sinx)=f[cos(π/2-x)]=cos[17(π/2-x)]
=cos(17π/2-17x)
=cos(π/2-17x)
=sin17x
(2)f(cosx)
=f[sin(π/2-x)]
=sin(4n+1)(π/2-x)
=sin[(4n+1)π/2-(4n+1)x]
=sin[2nπ+π/2-(4n+1)x]
=sin[π/2-(4n+1)x]
=cos(4n+1)x
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