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Find the range of the function 5sinx -12...

Find the range of the function `5sinx -12cosx +7`

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`f(x)=5sinx-12cosx+7`
`sqrt(a^2+b^2)/sqrt(a^2+b^2)(asinx++bcosx)`
`sqrt(a^2+b^2)(a/sqrt(a^2+b^2)sinx+b/sqrt(a^2+b^2)cosx)`
`sinalpha=a/sqrt(a^2+b^2)`
`cosalpha=b/sqrt(a^2+b^2)`
`sqrt(5^2+12^2)=sqrt(25+144)=sqrt169=13`
`13/13(5sinx-12cosx)+7`
`13(5/13sinx-12/13cosx)+7`
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