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Find the range of f(x)=sqrt(sin^2x-6sinx...

Find the range of `f(x)=sqrt(sin^2x-6sinx+9)+3`.

Text Solution

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`f(x)=sqrt(sin^2X-6sinx+9)+3`
`=sqrt((sinx-3)^2)+3`
`=abs(sinx-3)+3`
Now, `-1lesinxle1`
or `-4lesinx-3le-2`
or `2leabs(sinx-3)le4`
or `5leabs(sinx-3)+3le7`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
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