## Sbdenney Let sin A = 12/13 with 90º≤A≤180º and tan B = -4/3 with 270º≤B≤360º. Find tan (A + B). I need help PLEASE 2 years ago 2 years ago

1. Sbdenney

I need the fraction

2. Sbdenney

3. myininaya

$\tan(A+B)=\frac{\sin(A+B)}{\cos(A+B)}=\frac{\sin(A)\cos(B)+\sin(B)\cos(A)}{\cos(A)\cos(B)-\sin(A)\sin(B)}$ So we need to know the following: sin(A);sin(B);cos(A);cos(B) |dw:1323414397246:dw|

4. myininaya

we have two right triangles: we need to use Pythagorean thm twice

5. myininaya

|dw:1323414566260:dw|

6. myininaya

sin(A)=12/13;sin(B)=-3/5;cos(A)=-5/13;cos(B)=4/5

7. myininaya

so plug this into what I gave you above

8. myininaya

$\tan(A+B)=\frac{\sin(A+B)}{\cos(A+B)}=\frac{\sin(A)\cos(B)+\sin(B)\cos(A)}{\cos(A)\cos(B)-\sin(A)\sin(B)}$