一条函数题…y=2sin^2(x)－3cos(x)－1的值域是多少?谢々～

网友回答

y=2sin^2(x)－3cos(x)－1
=2[1-cos^2(x)]-3cos(x)-1
=-2cos^2(x)-3cos(x)+1
=-2[cos^2(x)+(3/2)cos(x)]+1
=-2[cos(x)+(3/4)]^2+(17/8)
∵ -1≤cosx≤1
∴ -4≤y≤17/8