SOLUTION: Write 5sin(t)-12cos(t) in the form of Asin(Bt+ϕ) using sum or difference formulas.

First,  5sin(t) - 12cos(t) = .   (1)



Second, the angle  does exist such that  =  and  = . 

    The rationality for it is the fact that  = 1.
    You can easily check this identity keeping in mind that  = .



Now, you can write (re-write) the formula (1) as follows

5sin(t) - 12cos(t) =  =  = .


Thus we presented  5sin(t) - 12cos(t) in the form    with A = 13,  B = 1,  and   =  = .