Final answer:
An example of the president acting as the chief diplomat through an executive agreement is when the c) president negotiates directly with a foreign leader on matters like nuclear disarmament, not requiring Senate approval.
Step-by-step explanation:
Chief Diplomat: Executive Agreements
When the president acts as the chief diplomat of the country, they make important decisions in the realm of foreign policy. One such decision is the creation of executive agreements, which are pacts made with foreign governments that do not require the Senate's approval, unlike formal treaties. An example of an executive agreement is when a president negotiates directly with the leader of another country on issues such as nuclear disarmament.
Option c) President Trump negotiates a reduction in nuclear weapons with Kim Jong-Un of North Korea would be a clear example of the president acting as chief diplomat, as it involves these direct negotiations. Such an agreement, if not submitted to the Senate for ratification, can be considered an executive agreement. This action fits within the constitutionally allowed powers of the president to extend their authority over foreign policy through these informal but binding agreements.