Final answer:
The sympathetic nerves may leave the spinal cord at the first thoracic vertebra (T1), which is the starting point of the thoracic region where the sympathetic chain ganglia begin. The other options presented are not the exit points for the sympathetic nerves in the spinal cord.
Step-by-step explanation:
The sympathetic nerves are part of the autonomic nervous system and influence various organ systems through connections that emerge from the thoracic and upper lumbar regions of the spinal cord. Specifically, these nerves are associated with the sympathetic chain ganglia, which are parallel to the vertebral column.
Vertebrae that give rise to sympathetic nerves include those in the thoracolumbar region, which encompasses all of the thoracic vertebrae (T1 to T12) and the upper lumbar vertebrae (L1 to L2). Therefore, the correct answer to the question "Sympathetic nerves may leave the spinal cord at which vertebrae?" is 4) first thoracic (T1), as this is the starting point of the thoracic region where the sympathetic chain ganglia begin.
The other options are incorrect because sympathetic fibers do not exit the spinal cord at the second cervical (C2), third lumbar (L3), or first coccygeal (Co1) levels.