Good day(evening?) everybody

I have two questions and I ain't sure which is more important right now:

1. this one is for school:
if all this is true:

tan(a)=-3/4
(90<a<180)
tan(b)=5/12
(0<b<90)

without using a calculator(meaning you musn't find out how much a and b are) what is the value of this expressions:

A. tan(a+b) , tan(a-b)
B. sin(a+b) , sin(a-b)
C. cos(a+b) , cos(a-b)


2. this one is for myself:
as we all know calculators know exactly how much cos(a) is. since the only value we input is a how the hell does it calculate cos(a)???????????????