Reflection: Developing a Conceptual Understanding Transformations of Sine and Cosine Graphs - Section 1: Warm-up and Homework Review


I think that horizontal shifts and period changes confuse students the most when dealing with graphs of sine and cosine.  With period, so often students want to say that the 2 in f(ϴ)=sin(2ϴ) makes the period twice as long which seems to intuitively makes sense.  If we have f(ϴ)=2sin(ϴ), this is twice as tall.  In fact, this has the same inverse operation effect as a horizontal shift so this was one approach I used when I taught this lesson.  Verbally, I also told my students that this meant twice as many curves in a 2π interval.  For those that struggled with the inverse operation concept, this seemed to help. 

I was pleased with the responses from this warm up.  I was expecting more students to be mistaken but most of the responses I received were like Warm Up 1 and Warm Up 2.  With today’s lesson that puts it all together, I hope that we will further solidify their knowledge of period and avoid this error.  

  Developing a Conceptual Understanding: Making Sense of Period
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Transformations of Sine and Cosine Graphs

Unit 9: Trigonometric Functions
Lesson 11 of 19

Objective: Students will be able to use transformations of functions to graph and write equations for sine and cosine functions.

Big Idea: How many equations can on trig function actually have? Here's a hint... it's a lot more than one.

  Print Lesson
Math, Trigonometry, Trigonometric functions, Algebra 2, Transformations of Functions, master teacher project, sine function, cosine function
  50 minutes
image transformations of sine and cosine
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