Final answer:
The use of logic, reason, and evidence to convince someone that cooperation is worthwhile is called rational appeals, and it relies on logos, the logical appeal.
Step-by-step explanation:
The tactic for influencing others that involves the use of logic, reason, and evidence to convince another person that cooperation in a task is worthwhile is known as rational appeals. This technique is underpinned by logos, which is an appeal to an audience's logical and rational thinking through the use of facts and data as evidence.
In practice, you would state your position clearly and support it with rational arguments, critical thinking, and credible evidence without exaggeration or unsupported claims. For example, a company might use a rational appeal by highlighting the safety features and fuel economy of their car to persuade customers, focusing on the quality of the information to affect a lasting attitude change.