In what way do the parasympathetic and the sympatheticnervous systems work together?

Answer 1

Yes. The vagus nerve is a parasympathetic nerve that is almost always stimulating the healthy heart to have a heart rate less than the inherent rate of the SA node.

The sympathetic innervation on the heart is minimal and only important during exercise.

Answer 2

Sympathetic neurons cause pacemaker cells to generate action potentials more frequently, and thus increase heart rate. In contrast, parasympathetic neurons have the opposite effect; they cause a decrease in the frequency of action potentials generated by peacemaker cells, and thus decrease heart rate. The heart simultaneously receives both sympathetic and parasympathetic signals in a "push-pull" manner. Increases in one are accompanied by decreases in the other.
SNS increases heart rate, contraction strength, etc, PSNS inhibits (i.e) slow down heart rate, decrease blood pressure, contraction strength, etc.

Answer 3

The affect that the parasympathetic nervous system has is that it decreases the heart. The result in terms of the cardiac output is that it decreases cardiac output.