Question

Find the maximum value of 5cosA + 12sinA + 12

Answer 1

5cosA +12sinA + 12 = 13(5/13 cosA +12/13sinA) + 12

Now, for any values of B we can get sinB = 5/13 and we can replace cosB = 12/13.

We see that our assumption is right because we satisfy the condition $sin^{2}$B + $cos^{2}$B = 1 so we get 13(sinBcosA +cosBsinA) + 12 =13(sin(A+B))+12.  

Therefore we know that minimum value of sinx=-1 and greatest is 1. Тhe greatest value is when sin(A + B) = 1 then value of the expression becomes 13.1 + 12 = 25