The range of $y = {sin}^{3} x - 6 {sin}^{2} x + 11 sin x - 6$ is

[- 24, 2]

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[- 24, 0]

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[0, 24]

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None of these

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Solution

The correct option is A $[- 24, 0]$
$y = {sin}^{3} x - 6 {sin}^{2} x + 11 sin x - 6$

Put $sin x = t$ ,
$y = t^{3} - 6 t^{2} + 11 t - 6, - 1 \leq t \leq 1$

From $- 1 \leq t \leq 1$ we know the maximum and minimum value of $t$

$f (- 1) = - 24$

$f (1) = 0$

$∴ R a n g e = (- 24, 0)$

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