Question

1. Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Sin(A+B).

a) 24/80
[b)] 84/85
c) 60/80
d) 60/85

Find Cos(A+B).

a) 32/80
b) -45/85
c) -13/80
[d)] -13/85

Find Tan(A+B)
a) 0.8
[b)] -1.72
c) -4.21
d) -6.46

I keep getting an 1.61 answer but that isn't an option?

What is the quadrant of A+B?
[a)] I
b) II
c) III
d) IV

Answer 1

I hope you got

sinA = 3/5
cosA = 4/5
tanA = 3/4

sinB = 15/17
cosB = 8/17
tanB = 15/8

given that, then

sin(A+B) = 3/5 * 8/17 + 4/5 * 15/17 = 84/85
cos(A+B) = 4/5 * 8/17 - 3/5 * 15/17 = -13/85
tan(A+B) = 84/-13 = -6.46
it might have been nice to see where you went wrong there.

since sin=y/r and z = x/r, we have
x<0 y>0, so QII

Answer 2

What are the answers to the first problems of a+b?