Tangent and Secant

Group members and roles: Please enter your group members' names as well as their role during this activity. (1) Recorder: This person should be managing the GGB file and typing your group's responses. (2) Reporter: This person is responsible to share out when we come together as a whole class. (3) Group monitor: Make sure that everyone is contributing, and no one is dominating the group. (Remember no one knows everything and everyone knows something.) (4) Task monitor: Make sure that the group is staying focused on the task at hand and help with the pacing.

Before you start, please answer the following questions without using any technology. (1) When is the tangent function 0? How do you know? (2) When is the tangent function undefined? How do you know?

Before you start, please answer the following questions without using any technology. (1) When is the secant function 0? How do you know? (2) When is the secant function undefined? How do you know?

Which line(s) did you need to turn on to find the segment that when related to the arc will create the tangent function?

Identify the segment for the tangent by identifying its endpoints and explain why this is the tangent.

Which line(s) did you need to turn on to find the segment that when related to the arc will create the secant function?

Identify the segment for the secant by identifying its endpoints and explain why this is the secant.

After you create the graphical representations, revisit (but don't edit) your responses to Q2 and Q3. Can you use the geometric interpretation to answer Q2 and Q3 differently? If so, explain.

The process of adding the lines to find or create the tangent and secant function is not easy. How would you describe the for a student who hasn't seen this before. How would you construct the two functions and use your constructions to create the graphical representation?