求下列函数的值域:(1)y=4-3sin(x-π/3) (2)y=cos^2x-sinx.
问题描述:
求下列函数的值域:(1)y=4-3sin(x-π/3) (2)y=cos^2x-sinx.
答
(1)y=4-3sin(x-π/3) x-π/3是整体,所以-1≤sin(x-π/3)≤1所以-3≤3sin(x-π/3)≤3 所以y=4-3sin(x-π/3) 的值域为[1,7](2)y=cos^2x-sinxy=(2cos^2x-1)/2+1/2-Sinx=cosx-sinx+1/2=√2cos(x+π/4 )+1/2 -1≤cos...