Graphing Trigonometric Functions

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SWBAT graph trigonometric (sine and cosine) functions by hand.

Big Idea

Students will apply their prior knowledge of shifting functions or the 5-point method to graph trigonometric functions.

Warm-up: Wrap up Shifting

5 minutes

If I was not able to wrap up the calculator activity during yesterday’s lesson, I will have students complete the clicker questions as a warm-up today. The summary clicker questions for shifting trigonometric functions are located on pages 7-11 of the Flipchart_Shifting Trig Functions.flipchart. I think it is important for students to have a solid understanding of how parameter changes on an equation affect the graph of trigonometric equation to aide in their ability to graph the functions by hand.  I find that some of my students will use this method to graph trig functions and others will use it to check their graphed equations for accuracy.

Graphing Trig Functions by Hand

35 minutes

In the middle part of today’s lesson, I plan to model for students a few different methods to graph trigonometric functions by hand. I think the most consistent and accurate method is to use the 5 Point Method. I am going to teach this as the primary method for graphing, but I will also show my students some other methods that will help them to check their work.

Every student will get a Graphing Trig Functions by hand handout. I want to scaffold their note taking as I model a few problems. Nonetheless, I want my students to take notes in their own words, to describe the steps of the 5-point method in their own language as we work together.

Once we have practiced the 5-point method, I will review the concept of shifting and have students check their answers by using their shifting knowledge. Also, I want to model for students the idea of a making a T table to graph trig functions (using angle inputs, find the output, plot the point). I find that students really like this method, but I caution them against using only this method because they need to be assured that they are picking the correct inputs to get a good representation of the graph. So, I really try to push my students to only check their answers using this method.

Closure: Practice Problems

10 minutes

For the last few minutes of class, I want students to practice graphing trig functions by hand. I will have them complete the last two problems on their Graphing Trig Functions by hand handout for today working independently. Then, I will review answers with the class before the students leave for the day.


Tonight I will assign Homework 8- Trigonometric Functions for homework.