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

Explanation

`f(theta) =5 cos theta +3 cos(theta + (pi)/(3))+3`
`=5 cos theta +(3)/(2)cos theta -(3sqrt(3))/(2)sin theta +3`
`=(13)/(2) cos theta - (3 sqrt(3))/(2)sin theta +3`
`=sqrt(((169)/(4)+(27)/(4)))sin (alpha-theta)+3`
`=7 sin(alpha- theta)+3`
Thus, the range of `f(theta)` is `[-4,10]`.