Curriculum / Math / 11th Grade / Unit 6: Unit Circle and Trigonometric Functions / Lesson 11
Math
Unit 6
11th Grade
Lesson 11 of 14
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Graph transformations of tangent functions.
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
For the first anchor problem, consider giving each table to a different group and then tiling the graphs together.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Calculate each value of $${\mathrm{tan}(x)}$$ to two decimal places for each of the charts below. Then, approximate the graph.
Algebra II > Module 2 > Topic B > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
For each set of expressions below, all expressions are equivalent. Explain why this makes sense.
$${\mathrm{tan}(\pi+x)}$$ and $${\mathrm{tan}(2\pi+x)}$$
$${\mathrm{tan}(-x)}$$ and $${\mathrm{tan}(\pi-x)}$$ and $${\mathrm{tan}(2\pi-x)}$$
Graph that function $${f(x)=-2\mathrm{tan}(x)}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
a. Sketch a graph of the function $${f(x)=\mathrm{tan}\left(\frac{x}{2}\right)}$$.
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b. What is the period of this function? Why?
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 10
Lesson 12
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
Graph transformations of sine and cosine functions (Part II).
F.BF.B.3 F.IF.C.7.E
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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