Find the minimum value of 5cosA + 12sinA + 12
Choose the correct option.
A) -1  B) 1  C) 2  D) 3  E) None of these
Solution:   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^2B + cos^2B=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 so the least value of the expression becomes when sin(-1+B) =-1 then the value of the whole term becomes 13.(-1) + 12 = -13 +12 = -1   -1nswer -1
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Find the minimum value of 5cosA + 12sinA + 12