Unit Circle and Trigonometric Functions

Lesson 3

Math

Unit 6

11th Grade

Lesson 3 of 14

Objective


Find values of specific points on the unit circle using geometry.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • G.SRT.D.10
  • G.SRT.D.11
  • G.SRT.D.9

Criteria for Success


  1. Identify 30-60-90 and 45-45-90 triangles in the unit circle.
  2. Find coordinates of points at reference angles on the unit circle.
  3. Identify reference angles on a unit circle and explain their geometric significance.
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Anchor Problems


Problem 1

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 $${45^{\circ}}$$.

Guiding Questions

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Problem 2

The radius of the circle above is $$1$$, and it is centered at the origin. Find the coordinates of the point marked at $$150^{\circ}$$.

Guiding Questions

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Target Task


Find the distance between the point labeled $${30^{\circ}}$$ and the point labeled $$3{30^{\circ}}$$.

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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Trigonometric Ratios in Application and on the Unit Circle

Topic B: Graphing Sine, Cosine, and Target

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