Find the minimum and maximum values of the function f(x)= a cos x+ b sin x (a^2 +b^2 >0)

Answers (1)

Solution:   The given function can be represented as:

                            f(x)=acos x+bsin x=sqrta^2+b^2cos (x-alpha)

       where hspace0.2cmcos alpha =fracasqrta^2+b^2;sin alpha =fracbsqrta^2+b^2hspace0.2cmSince, hspace0.2cmleft | cos (x-alpha ) 
ight |leq 1

    The maximum value of      f(x)=+sqrta^2+b^2(at hspace0.2cmcos(x-alpha)=1)

    The minimum value of       f(x)=-sqrta^2+b^2(at hspace0.2cmcos(x-alpha)=-1)    

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