Question

求函数y=3cos^2x+9sinx-7/4的值域

Answer 1

y=3cos^2x+9sinx-7/4

=3(1-sin^2x)+9sinx-7/4

=-3sin^2x+9sinx+3-7/4

=-3(sinx-3/2)^2+27/4+5/4

=-3(sinx-3/2)^2+8

当sinx=1时有最大值,是y=29/4

当sinx=-1时有最小值,是y=-43/4

即值域是[-43/4,29/4]