In sin(a-b) = sin(a)cos(b)-cos(a)sin(b), the minus sign is provided, so

b is not -5pi/3;  instead,  it is simply 5pi/3  [ it might help to think of it as a pattern match. You are subtracting one angle from another, but both those angles have their own signs. ]



cos(b) is 

sin(b) is -



resulting in 





Although you had the sign error, there was also an error in how you simplified the expression-- you somehow lost the 1/26 from the first term.  Note that sin() and cos() will always produce outputs between -1 and +1 inclusive.  The "5+" in your answer is an immediate indication that something is wrong. 



But, I want to congratulate you on your effort.  Not many students post their work here and it is refreshing to see... AND an "A" for your approach.  





EDIT: I fixed the sin(a-b) formula and two missing minus signs, result is the same.





 

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