HSF-TF.A.2

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- HSF-TF.A.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- HSF-TF.A.2Explain 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.
- HSF-TF.A.3(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.
- HSF-TF.A.4(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

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## HSF-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.

70 Lesson(s)

### Graphs of Sine and Cosine

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### Students get to build the graph of sine or cosine with yarn and spaghetti.

Standards:

Favorites
(10)

Resources
(47)

Reflections
(4)

Big Idea:

#### Radian rotation-style review of radians and radian measurement.

Standards:

Favorites
(3)

Resources
(8)

### What do Triangles have to do with Circles?

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### How is the unit circle related to "triangle measurement"? A story of two equivalent definitions.

Standards:

Favorites
(10)

Resources
(17)

Reflections
(1)

### Introduction to the Ferris Wheel Problem

12th Grade Math »
Unit: Ferris Wheels

12th Grade Math »
Unit: Ferris Wheels

Big Idea:

#### You are riding a Ferris wheel near the Golden Gate Bridge. When will you be high enough to see the full view? Students attempt to answer this question using some knowledge of right triangles.

Standards:

Favorites
(8)

Resources
(9)

### The Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### The unit circle allows us to extend the trigonometric functions beyond the confines of a right triangle.

Standards:

Favorites
(7)

Resources
(18)

Reflections
(1)

### Ferris Wheel (Graph) Symmetries

12th Grade Math »
Unit: Ferris Wheels

12th Grade Math »
Unit: Ferris Wheels

Big Idea:

#### You are sitting on a Ferris wheel. Who is directly across from you? Below you? Diagonally across from you? Use a representation of the unit circle to make generalizations.

Standards:

Favorites
(4)

Resources
(11)

### Solving Trig Equations

12th Grade Math »
Unit: Trigonometric Relationships

12th Grade Math »
Unit: Trigonometric Relationships

Big Idea:

#### Why do these trig equations have so many solutions?

Standards:

Resources
(18)

Reflections
(2)

### The Unit Circle Day 2 of 2

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### Why do we use a unit circle? How can we use it to represent all angles for all circles?

Standards:

Favorites
(4)

Resources
(24)

### Introducing: Radians!

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### Why should we divide the circle into 360 parts? Isn't there a more natural unit? Yes - the radius!

Standards:

Favorites
(7)

Resources
(13)

Reflections
(1)

### Midterm Review Workshop

12th Grade Math »
Unit: Midterm Review and Exam

12th Grade Math »
Unit: Midterm Review and Exam

Big Idea:

#### Students work on midterm review and let you know what they still need help with.

Standards:

Resources
(3)

### The Unit Circle Day 1 of 2

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### Why do we use a unit circle? How can we use it to represent all angles for all circles?

Standards:

Favorites
(6)

Resources
(26)

### Angle and Degree Measure

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### Students will turn a locker combination into a secret math code (angles).

Standards:

Favorites
(10)

Resources
(28)

Reflections
(1)

Big Idea:

#### How do I even start this problem?! Give your students tools to help make sense of and work with trig problems.

Standards:

Favorites
(5)

Resources
(10)

### Trigonometric Ratios

Algebra II »
Unit: Trigonometric Functions

Algebra II »
Unit: Trigonometric Functions

Big Idea:

#### Students will review and extend their knowledge of trigonometric ratios.

Standards:

Favorites
(3)

Resources
(22)

Reflections
(1)

Big Idea:

#### Radians are radical! Use them to make working with trig ratios easier.

Standards:

Favorites
(2)

Resources
(14)

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