若函数y=(sinx)^2+acosx+5a/8-3/2(0
问题描述:
若函数y=(sinx)^2+acosx+5a/8-3/2(0
答
y=sinxsinx+acosx+5a/8-3/2 y=1-cosxcosx+acosx+5a/8-3/2y=-cosxcosx+acosx+5a/8-1/2y=-[cosx-a/2]^2 +a^2/4+5a/8-1/2∵x∈[0,∏/2] ∴cosx∈[0,1] 令t=cosx ,则t∈[0,1] 则y=f(t)=-[t-a/2]^2 +a^2/4+5a/8-1/2 ,t∈[...