Curriculum / Math / 11th Grade / Unit 6: Unit Circle and Trigonometric Functions / Lesson 10
Math
Unit 6
11th Grade
Lesson 10 of 14
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Graph transformations of sine and cosine functions (Part II).
The core standards covered in this lesson
F.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
F.IF.C.7.E — Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Show students Graph 21 from Which One Doesn't Belong: Graphs and Equations.
Which One Doesn't Belong is made available on Which One Doesn't Belong?. Copyright © 2013 wwdb.ca. All Rights Reserved. Accessed on Dec. 12, 2016, 1:35 p.m..
Do this Desmos activity, Sine Transformations, with students.
Sine Transformations by Jeremy Babel is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed Feb. 26, 2018, 3:43 p.m..
Write both a sine and cosine function that model the graph shown below.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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$${y=-3\mathrm{sin}(2x)+3}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 9
Lesson 11
Topic A: Trigonometric Ratios in Application and on the Unit Circle
Sketch sine graphs to model contextual situations and identify features of sine graphs.
F.IF.B.4 F.IF.C.7.E F.TF.A.4 F.TF.B.5
Sketch cosine graphs to model contextual situations and identify features of cosine graphs.
F.IF.B.4 F.IF.C.7.E F.TF.B.5
Find values of specific points on the unit circle using geometry.
F.TF.A.2 F.TF.A.4
Evaluate sines and cosines of points at reference angles on the unit circle.
Describe the relationship between the unit circle and tangent.
F.TF.A.2 F.TF.A.3
Define and evaluate the trigonometric functions of tangent, cosecant, secant, and cotangent.
Convert between degrees and radians and evaluate trigonometric functions written in radians.
F.TF.A.1 F.TF.A.3
Evaluate transformations of sine, cosine, and tangent such as $${2{\pi-x}}$$, $${\pi-x}$$, and $${\pi+x}$$.
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Topic B: Graphing Sine, Cosine, and Target
Graph transformations of sine and cosine functions (Part I).
F.IF.C.7.E F.TF.A.1 F.TF.A.3 F.TF.A.4
F.BF.B.3 F.IF.C.7.E
Graph transformations of tangent functions.
Identify equations and graphs of all six trigonometric functions.
F.BF.B.3 F.TF.A.3 F.TF.B.5
Model contextual situations using trigonometric functions (Part I).
F.TF.A.3 F.TF.B.5
Model contextual situations using trigonometric functions (Part II).
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