Activity Overview
This lesson provides opportunities for students to explore graphs of the cotangent, secant, and cosecant functions by observing the changes in function values for cotangent, secant, and cosecant, and observing the connections to the graphs of each of the three functions.
Objectives
• Students will be able to identify the values of cotangent, secant and cosecant for various values of θ from the unit circle.
• Students will understand the correspondence of the graphs of cotangent, secant and cosecant to the unit circle.
• Students will be able to identify and explain features of the graphs of cotangent, secant, and cosecant, particularly locations where the functions are undefined, or where they have intercepts.
Vocabulary
• Sine
• Cosine
• Cotangent
• Secant
• Cosecant
• Unit circle
About the Lesson
• This lesson provides opportunities for students to explore and make sense of the graphs of the cotangent, secant, and cosecant functions.
• Students use clickers to move a point around the unit circle, observing the changes in function values for cotangent, secant, and cosecant, and observing the connections to the graphs of each of the three functions.
• The lesson provides opportunities to make and test conjectures about the graphs of the cotangent, secant, and cosecant functions based on observations from the unit circle.