Curriculum / Math / 11th Grade / Unit 6: Unit Circle and Trigonometric Functions / Lesson 4
Math
Unit 6
11th Grade
Lesson 4 of 14
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Evaluate sines and cosines of points at reference angles on the unit circle.
The core standards covered in this lesson
F.TF.A.2 — Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
F.TF.A.4 — Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
The foundational standards covered in this lesson
G.SRT.D.10 — Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.D.11 — Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
G.SRT.D.9 — Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Below is a diagram of a Ferris wheel. It is a model with a one-foot radius.
Assume that a person enters onto the Ferris wheel at the position You and travels a turn of $${30^{\circ}}$$ round the center point.
What are the sine and cosine for each degree turn shown below?
In the unit circles we have been looking at, $${0^{\circ}}$$ and $$36{0^{\circ}}$$ are marked in the same place. What other angles are equivalent to $$3{0^{\circ}}$$? $$7{0^{\circ}}$$? What angle on the unit circle is equivalent to $${495^{\circ}}$$?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Calculate $${\mathrm{sin}(210^{\circ})}$$ and $${\mathrm{cos}(210^{\circ})}$$ without a calculator.
Algebra II > Module 2 > Topic A > Lesson 4 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..
Evaluate $${\mathrm{sin}(-90^{\circ})}$$ without a calculator.
Calculate $${\mathrm{cos}(480^{\circ})}$$ and $${\mathrm{sin}(480^{\circ})}$$ without a calculator.
Algebra II > Module 2 > Topic A > Lesson 5 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..
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.
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Describe the relationship between the unit circle and tangent.
Topic A: Trigonometric Ratios in Application and on the Unit Circle
Sketch sine graphs to model contextual situations and identify features of sine graphs.
Standards
F.IF.B.4F.IF.C.7.EF.TF.A.4F.TF.B.5
Sketch cosine graphs to model contextual situations and identify features of cosine graphs.
F.IF.B.4F.IF.C.7.EF.TF.B.5
Find values of specific points on the unit circle using geometry.
F.TF.A.2F.TF.A.4
F.TF.A.2F.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.1F.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.EF.TF.A.1F.TF.A.3F.TF.A.4
Graph transformations of sine and cosine functions (Part II).
F.BF.B.3F.IF.C.7.E
Graph transformations of tangent functions.
Identify equations and graphs of all six trigonometric functions.
F.BF.B.3F.TF.A.3F.TF.B.5
Model contextual situations using trigonometric functions (Part I).
F.TF.A.3F.TF.B.5
Model contextual situations using trigonometric functions (Part II).
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