Find the range of `f(theta) = 5 costheta + 3 cos(theta + pi/3) + 3 `

Explanation

`f(theta) = 5costheta+3cos(theta+pi/3)+3`

`=>f(theta) = 5costheta + 3(costhetacospi/3-sinthetasinpi/3)+3`

`=>f(theta) = 5costheta + 3(costheta(1/2)-sintheta(sqrt3/2))+3`

`=>f(theta) = 5costheta + 3/2costheta-(3sqrt3)/2sintheta+3`

`=>f(theta) = 13/2costheta-(3sqrt3)/2sintheta+3`

We know, for a function `f(x) = acosx+bsinx+c`,

`f(x)_max = c + sqrt(a^2+b^2)`

`f(x)_min = c - sqrt(a^2+b^2)`

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