Final answer:
The exact value of (a - b) is found by calculating the angles given by arcsin(4/5) and arccos(8/17) and then subtracting them.
Step-by-step explanation:
The exact value of (a - b) where angle a is arcsin (4/5) and angle b is arccos(8/17) can be found by calculating each angle in radians or degrees and then subtracting them. Note that the arcsine function gives you the angle whose sine is the provided value, while the arccosine function gives you the angle whose cosine is the provided value.
Therefore, we can understand angle a as the angle in a right triangle where the opposite side is 4 and the hypotenuse is 5, and angle b as the angle in another right triangle where the adjacent side is 8 and the hypotenuse is 17.
To find the exact values for a and b, you would typically use a calculator or trigonometric tables since they are not among special angles we know the exact trigonometric ratios for. After finding these values, we simply compute a minus b to get the exact difference between the two angles.