Step by Step of this pre trig questionplease

Question

I really need helping understanding this, can someone please give me a step by step of this problem. thanks.

 

Find cos(a+b) if sin(a)=-3/5 where a is in the fourth quadrant and tan(b)=12/5 where b is in the third quadrant. 

Answer 1

form a right triangle

sina=-3/5 in the 4th quadrant

sin=opp/hyp, therefore the adjacent side is 4

cosa=adj/hyp

cosa=4/5 and cos is positive in the fourth quadrant

 

tan=opp/adj

tanb=12/5

form a right tringle

if opp is 12 and adj is 5, then hyp=13 by Pythagorean Theorem

sinb=12/13 and sin is negative in 3rd quadrant so...

sinb=-12/13

cosb=-5/13 by same reasoning (cos negative in 3rd quadrant)

 

cos(a+b)=cosacosb-sinasinb

cos(a+b)=(4/5)(-5/13)-(-3/5)(-12/13)

cos(a+b)=(-20/65)-(36/65)

cos(a+b)=(-56/65)