Final answer:
To open the mouth of the fetal pig to view the nasopharynx, the temporomandibular joint (TMJ) must be dislocated, which involves a downward hinging and anterior gliding motion of the mandible.
Step-by-step explanation:
The joint that must be dislocated in order to open the mouth of the fetal pig to view the nasopharynx is the temporomandibular joint (TMJ).
This joint allows for the opening (mandibular depression) and closing (mandibular elevation) of the mouth through a combination of motions.
When opening the mouth, an initial downward hinging of the mandible occurs in combination with an anterior gliding motion of both the mandible and the articular disc.
These combined actions result in the mandibular condyle and the articular disc gliding forward from the mandibular fossa onto the articular tubercle.