Shifting Trig Functions - Student Discovery

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SWBAT shift, shrink, and stretch trig functions graphs starting with the parent function.

Big Idea

Students collaborate to create a flip-chart poster and compare/contrast transformations of sine and cosine functions.

Entry Slip - Setting the Stage

10 minutes

As the students enter the classroom for today, I ask them to take out their notes (that they did yesterday's homework in) and I circulate the Entry Slip - Trig Functions.  Please note that the entry slip has two sides and is intended to be copied front and back.  As the students work on the entry slip, I ask them to respond to the questions silently while I rotate the room and see who properly attempted their assignment. I make note of the students who failed to complete the task, and talk briefly with these students 1-1. In my experience, part of coaching kids in an upper level math class involves getting them used to "non-traditional" homework assignments.  Last night's homework is a prime example. Since it was not a worksheet, it shifts the responsibility to the student as I simply asked them to make additions to their class notes. I suspect many students will not feel that it is important to complete the task.  I coach them through this and explain the importance of keeping up.  It is always good to have the discussion with kids that we don't give homework just for the sake of giving homework.  I give homework to complete a task that we did not have in class and/or to practice a skill that we learned.  Once the students understand this and hear it (sometimes multiple times) they begin to realize that the teacher really is on their side.  With this said, I try to be careful to NEVER assign homework as a punishment.  It only takes doing this once to turn the homework experience for a student from something practical and positive to something that is not learning-centered. 

Poster Discoveries

20 minutes


  • Groups of 2-3 students
  • Easels
  • Markers


How this activity works:  The students work with the slider website to generate a basic trig graph that matches one that I have selected off of the bell work (any of the back side ones are best).  Once the students have this accomplished, they are then asked to graph it (with the sliders) as an alternate trig function.  This shows the students that the sine can be used as a shifted graph of the cosine and visa-versa.  An overview of this activity is discussed in the video narrative.

Poster Presentations

10 minutes


After wrapping up their findings and completing their posters, have the groups meet with another group who outlined a different function, that is, sine groups meet with cosine groups and visa-versa.  During this time, I ask the students to take turns sharing out their findings.  I rotate the room as students enter into mathematical conversations comparing and contrasting the results (MP3).  The Sharing Conclusions Sheet  helps guide the conversations and ensures they make the conceptual connections and learn from each other.  I felt a little awkward at first totally letting go of the steering wheel, but when the students take center stage in their learning it is so much more powerful and helps develop a vibrant shared learning community culture.

Homework + "PIXAR Movie Trailer" Exit Slip

5 minutes

In the event that the students do not complete the Sharing Conclusions Sheet, I have them complete this as a homework assignment for the following day.

If the students all finish the sharing conclusions sheet, then I wrap up class with a discussion of the learning for the day.  (Emphasis on the following:  Can a graph be BOTH a sine function and a cosine function?)   If the students are struggling with this, it might be helpful in the last couple of minutes to connect the lesson back to the unit circle.  I quickly draw an angle on the board mapped out by the circle and have my students tell me about the sine and cosine of the angle.  Because the angle has both a sine and a cosine, we should be able to write them as functions of each.  Therefore, there will be a sine and a cosine version of our trigonometric graphs - - they will simply be shifted on the axis. 


A new thing to try as a fun Exit Ticket.  In the exit slip, the students fill in the blanks of a movie-trailer style storyline.  I have never tried this before, but I anticipate getting a big kick out of the results!  High school kids can be very creative, plus, it forces them to reflect on their learning as they write.