f(x)=-cos^2x+simx+2,f(x)的值域是

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f(x)=-cos^2x+simx+2,f(x)的值域是
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f(x)=-cos^2x+simx+2,f(x)的值域是
f(x)=-cos^2x+simx+2,f(x)的值域是

f(x)=-cos^2x+simx+2,f(x)的值域是
f(x)=-[1-sin²x]+sinx+2=sin²x+sinx+1=[sinx+(1/2)]²+3/4.由于-1≤sinx≤1,则-1/2≤sinx+(1/2)≤3/2,所以0≤[sinx+(1/4)]²≤9/4,则原函数的值域是[3/4,3].

f(x)=-cos^2x+sinx+2 可以变成f(x)=sin^2X+sinX+1=(sinx+1/2)^2+3/4
值域[3/4,3]