Addition Formulas- Trig

[KingAce]

sin A= -4/5 cosB= -5/13

Problem: Find sin(A+B)
Problem 2: Find cos(A+B)

-I realize to find sin(A+B), I must use the formula, sinAcosB + cosAsinB
and to Find cos(A+B), I should use the formula, cosAcosB-sinAsinB

But how do I find sin B and cos A, for example? Thanks for your help

 

[morson]

Use the Pythagorean identity: (SinB)^2 + (CosB)^2 = 1

 

[skeeter]

sin A= -4/5 cosB= -5/13

Problem: Find sin(A+B)
Problem 2: Find cos(A+B)

-I realize to find sin(A+B), I must use the formula, sinAcosB + cosAsinB
and to Find cos(A+B), I should use the formula, cosAcosB-sinAsinB

But how do I find sin B and cos A, for example? Thanks for your help

the values depend on what quadrants angles A and B are in ...

sin(A) = -4/5 ... cos(A) is -3/5 (if A is in quad III) or 3/5 (if A is in quad IV)

cos(B) = -5/13 ... sin(B) is -12/13 (if B is in quad III) or 12/13 (if B is in quad II)