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Graphing Sine and Cosine Trig Functions with and without Phase Shifts
We will graph cosine and sine functions and identify the amplitude, period, and phase shift.
How are the standards/objectives assessed?
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
CCSS.MATH.CONTENT.HSF.IF.C.7.E
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Lesson Conclusion/Summary:
Students will use Desmos to create a system of graphs that includes the following:

Parent function (sine or cosine)

Transformation of the parent function without a phase shift

Transformation of the parent function with a phase shift to the right

Horizontal stretch or compression of the parent function with a phase shift to the left
Students will take a screenshot of their graphs on Desmos and attach it to a Google Form document. On the document, students will identify the amplitude and period for each function, then explain what their transformations and phase shifts did to the original graph of the parent function. Students will then turn this document into the posted assignment in Google Classroom. You can see my example system below. (You will need to use the link to view the sample system.)
Assessment: Formative /Summative:
I will use the lesson summary Desmos activity as the formative assessment and our summative assessment will be a quiz over sections 5.15.3.
FollowUp Lesson(s):
The following day, we will do the lesson conclusion using Desmos. Over the next few days, we will continue by reviewing for and taking our Quiz over sections 5.15.3, which will assess the standards listed above. The next section 5.4, will focus on graphing other trigonometric graphs. This will include graphing tangent, cotangent, secant, and cosecant functions.
Student prerequisite skills and knowledge
Students will need Algebra 2 as a prerequisite course.
How is the concept or procedure explained or demonstrated?
Introduction/WarmUp:
Students will use the Today’s Meet website to type in what they already know about sine and cosine graphs. I will let them use their own personal devices to access the website. If you’ve never used Today’s Meet before, this video can help you get started!
Procedure/Activities:
Day 1 (Introduction): Students will complete the Graphs of Sine and Cosine packet. This packet will introduce students to the concepts of amplitude and period, as well as explore translations and vertical stretches of sine and cosine graphs.
Day 2 (Section 5.3Day 1): Students will take notes with me using their notetaking guide for 5.3 Day 1 and complete the assigned homework problems. This section will require students to graph transformations of sine and cosine graphs (without phase shifts). They will also identify the amplitude and period of the graphs. (For the completed guide, see the link in the materials section.)
Day 3 (Section 5.3Day 2): Students will take notes with me using their notetaking guide for 5.3 Day 2 and complete the assigned homework problems. (For the completed guide, see the link in the materials section.) Today, we will extend graphing transformations of sine and cosine graphs by including phase shifts. I have a video series taken from class of me teaching this lesson. The phase shifts can be tricky for students, so I like them to have a resource they can refer to later. There are five videos for 5.3 Day 2, which I’ve organized in a playlist on my YouTube channel.
Lesson Conclusion/Summary:
Students will use Desmos to create a system of graphs that includes the following:

Parent function (sine or cosine)

Transformation of the parent function without a phase shift

Transformation of the parent function with a phase shift to the right

Horizontal stretch or compression of the parent function with a phase shift to the left
Students will take a screenshot of their graphs on Desmos and attach it to a Google Form document. On the document, students will identify the amplitude and period for each function, then explain what their transformations and phase shifts did to the original graph of the parent function. Students will then turn this document into the posted assignment in Google Classroom. You can see my example system below.
Lesson Conclusion/Summary:
Students will use Desmos to create a system of graphs that includes the following:

Parent function (sine or cosine)

Transformation of the parent function without a phase shift

Transformation of the parent function with a phase shift to the right

Horizontal stretch or compression of the parent function with a phase shift to the left
Students will take a screenshot of their graphs on Desmos and attach it to a Google Form document. On the document, students will identify the amplitude and period for each function, then explain what their transformations and phase shifts did to the original graph of the parent function. Students will then turn this document into the posted assignment in Google Classroom. You can see my example system below. (You will need to use the link above to view).
Assessment: Formative /Summative:
I will use the lesson summary Desmos activity as the formative assessment and our summative assessment will be a quiz over sections 5.15.3.
FollowUp Lesson(s):
The following day, we will do the lesson conclusion using Desmos. Over the next few days, we will continue by reviewing for and taking our Quiz over sections 5.15.3. The next section 5.4, will focus on graphing other trigonometric graphs. This will include graphing tangent, cotangent, secant, and cosecant functions.
What concepts or procedures are being explained or demonstrated in this lesson object?
Day 1 (Introduction): Students will complete the Graphs of Sine and Cosine packet. This packet will introduce students to the concepts of amplitude and period, as well as explore translations and vertical stretches of sine and cosine graphs.
Day 2 (Section 5.3Day 1): Students will take notes with me using their notetaking guide for 5.3 Day 1 and complete the assigned homework problems. This section will require students to graph transformations of sine and cosine graphs (without phase shifts). They will also identify the amplitude and period of the graphs. (For the completed guide, see the link in the materials section.)
Day 3 (Section 5.3Day 2): Students will take notes with me using their notetaking guide for 5.3 Day 2 and complete the assigned homework problems. (For the completed guide, see the link in the materials section.) Today, we will extend graphing transformations of sine and cosine graphs by including phase shifts. I have a video series taken from class of me teaching this lesson. The phase shifts can be tricky for students, so I like them to have a resource they can refer to later. There are five videos for 5.3 Day 2, which I’ve organized in a playlist on my YouTube channel.
What was your experience, both successes and challenges, using this lesson object with your students?
Reflection: Breaking this lesson into three days I think is very helpful for the students to process the new information. My students had been introduced to sine and cosine graphs in Algebra 2 Honors, but have never done phase shifts or explored the connections to the Unit Circle in great depth.. Doing the introduction worksheet without a calculator forces them to make the connections with the Unit Circle, which is nice to see. The second day, we introduce the concepts of transformations and how those affect the amplitude and period of the graph. Finally, concentrating on the phase shifts the final day gives the students time to process this challenging concept. I definitely recommend teaching them to take the period and divide it by four to make their xaxis scale for the phase shift graphs. We use the trig graph paper, which I included in the lesson, to help make our graphs neat so I would recommend that, as well. The students also enjoyed working with Desmos for their lesson wrapup!