Curriculum / Math / 11th Grade / Unit 6: Unit Circle and Trigonometric Functions / Lesson 3
Math
Unit 6
11th Grade
Lesson 3 of 14
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Lesson Notes
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Find values of specific points on the unit circle using geometry.
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
The radius of the circle above is $$1$$, and it is centered at the origin. This is called a “unit circle.” Find the coordinates of the point marked at $${45^{\circ}}$$.
The radius of the circle above is $$1$$, and it is centered at the origin. Find the coordinates of the point marked at $$150^{\circ}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find the distance between the point labeled $${30^{\circ}}$$ and the point labeled $$3{30^{\circ}}$$.
Next
Evaluate sines and cosines of points at reference angles on the unit circle.
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
F.TF.A.2F.TF.A.4
Describe the relationship between the unit circle and tangent.
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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