Find the maximum and minimum value of `5 cos theta +12 sin theta +12`

Explanation

`5 cos theta + 12 sin theta `

`sqrt(5^2 +12^2){5/sqrt(5^2 + 12^2) cos theta + 12/sqrt(5^2 + 12^2) sin theta}`

`sin phi = 5/sqrt(5^2 + 12^2)= 5/13`

`cos phi = 12/13 = 12/sqrt(5^2 + 12^2)`

putting it in the equation

`13{ sin phi cos theta + cos phi son theta}`

`= 13 sin( theta + phi)`

`= 12 + 13 sin( theta + phi)`

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