I own the Trike model listed above, I bought this Trike about 10 years ago, and I'm starting riding again but since the manuals are not very users friendly, I need to know the purpose of the 3 position knob for on the left handle?
Based on the specs at https://bicycleman.com/sun-ez-3-ez-3-ltd-recumbent-trike/ your trike has a triple front chainring and a 7 speed cassette in the rear.
The three-position control will be to adjust the front chainring while riding, so the bigger one is "harder" and the smaller one is "easier" Which one you choose depends on the terrain, but the middle or bigger chainrings are common, with the middle and smaller ones used on slower climbs.
Your right-side handlebar will have a 7 position shifter for the cassette at the rear. This is more of a fine control, whereas the chainrings are a coarse control.
In automotive terms, the rear cassette is a gearbox, and the chainrings are a transfer case letting you select between high-box, middle-box, and low-box. If manual truck transmissions are confusing, just ignore this paragraph :)
Aside - your bike may have "parking brakes" too, which is relatively unusual for a bicycle. Pressing the button on the brake levers will hold them in place, stopping the trike from rolling away. You wouldn't want to press them while riding.