Find the maximum value of the `5 sinx+12cosx`

Explanation

Let `5=rcostheta, 12=rsintheta`
`therefore5^2=r^2cos^2theta, 12^2=r^2sin^2theta`
`therefore5^2+12^2=r^2(cos^2theta+sin^2theta)=r^2`
`thereforer=(sqrt25+144)=13`
`therefore` themaximum value of `5 sinx+12cosx` is 13