In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Quadrant III:
cos (A) = -15 / 17
Step 02:
trig ratio:
cos θ = adjacent / hypotenuse
cos A = - 15 / 17
right triangle:
adjacent = 15
hypotenuse = 17
c² = a² + b²
17² = (15)² + (b)²
289 = 225 + b²
289 - 225 = b²
[tex]\begin{gathered} \sqrt[]{64}\text{ = b} \\ 8\text{ = b} \end{gathered}[/tex]opposite: 8
Quadrant III:
adjacent = -15
hypotenuse = 17
opposite = - 8
sin A = opposite / hypotenuse
sin A = - 8 / 17
sin (A - B):
[tex]\sin \text{ (A -B)=}\frac{-8}{17}-\frac{4}{5}=\frac{-40-68}{85}=-\frac{108}{85}[/tex]The answer is:
sin (A - B) = - 108 / 85
