Given that sin A = 4/5 and cos B = -1/3, and that A and B are in the same quadrant, without finding the angles A and B, find the value of sin (A+B). Thanks a lot
Hello, Leo!
Sine is positive in Quadrants 1 and 2.Given that: . and that and are in the same quadrant,
without finding the angles and , find the value of
Cosine is negative in Quadrants 2 and 3.
. . Hence, angles and are in Quadrant 2.
We have: . in Quadrant 2.
Since , we have: .
. .
Since is in Quadrant 2: .
We have: . in Quadrant 2.
Since , we have: .
. .
Since is in Quadrant 2: .
We know that: .
Substitute: .