Answer:
sin(α+β) = -13/85
Step-by-step explanation:
If 180°<α<270°, cos α=−8/17, 270°<β<360°, and sin β=−4/5, what is sin(α+β)?
We should use the trig formula for sin(α+β)
sin(α+β) = (sin α) (cos β) + (cos α)(sin β)
the hypotenuse is 17.... use Pythagorean theorem 8^2 + x^2 = 17^2
x= 15
then sin ( alpha) = -15/17
cos β = 3/5 since cosine is positive in the 4rth quadrant
and from the 3-4-5 triangle
sin(α+β) = (sin α) (cos β) + (cos α)(sin β)
sin(α+β) = (-15/17)*(3/5) + (-8/17) *(-4/5)
sin(α+β) = [ -45 + 32 ] / 85 = -13/85
sin(α+β) = -13/85
