This lecture covers the definitions and properties of the arctan and arccot functions, including their graphs and notable values. It explains the relationship between these functions and their respective trigonometric counterparts, as well as how to restrict them to specific intervals. The instructor emphasizes the importance of understanding the inverse trigonometric functions and provides insights into their graphical representations. The lecture concludes with a discussion on the graphs of arctan and arccot functions, highlighting key takeaways and preparing students for practical examples.