Find: sin (s+t), cos (s-t), tan (s+t), the quadrant of (s+t) 
Given:  and  and that s∈QI and t∈QIII


For my work I started off with sum and difference identities 

for ==== sin (s+t)
 
sin (s+t)=      <<<---=== cos(t) = -5/13
sin (s+t)= 
sin (s+t) =                    <<<---===  correct

for ==== cos (s-t) 
 
cos (s-t) =  
cos (s-t) =                   <<<---===  correct

for ==== tan (s+t)
    <<<---=== tan(t) = 12/5,   and FIX everything that follows
tan (s+t) = 
tan (s+t) = 

for quadrant of (s+t) I would infer Q2.  

from my work I think I messed up on sin t = -12/13 with the negative symbols, but I'm not sure and any help would be appreciated!