S.O.S. Mathematics CyberBoard

The problem is: Solve 6.5 - 5cos x - sin x. Where 0 =< x <= 2pi
I began by converting the trig part into a wave equation
- 5 cos x - 12 sin x = k cos (x - a)
k = 13
sin a = -12
cos a = - 5
tan a = 2.4
a = 1.176
Constructing the equation:
13 cos (x - 1.176) = - 6.5
cos (x - 1.176) = -6.5/13
x - 1.176 = 2.092 or 4.189
x = 3.27 or 5.37
But actual answer is:
x = 0.13 and 2.22
Can you please advise me where I am going wrong?

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Sandi Forrester