Question 1159666
<pre>
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 {{{ 1/2 }}}
sin(b) is -{{{sqrt(3)/2}}}

resulting in 
{{{ (-5/13)(1/2) - (-12/13)(-sqrt(3)/2) = red( (-1)(5+12*sqrt(3))/26 )}}}

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.