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Find the range of y=sin^3x-6sin^2x+11sin...

Find the range of `y=sin^3x-6sin^2x+11sinx-6.`

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`y=sin^3x-6sin^2x+11sinx-6`
Put `sinx=t`
`:. y=t^3-6t^2+11t-6,-1letle1`
`:. dy/dt=3t^2-12t+11`
`=3(t-2)^2-1gt0" for "-1letle1`
`:.` Function is increasing.
Hence, range is `[f(-1),f(1)]" or " [-24,0]`.
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