# Ch 10: Common Core HS Functions - Trigonometric Functions

### About This Chapter

**Standard**: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. (CCSS.Math.Content.HSF-IF.C.7e)

**Standard**: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. (CCSS.Math.Content.HSF-TF.A.1)

**Standard**: 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. (CCSS.Math.Content.HSF-TF.A.2)

**Standard**: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for x, pi + x, and 2pi - x in terms of their values for x, where x is any real number. (CCSS.Math.Content.HSF-TF.A.3)

**Standard**: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. (CCSS.Math.Content.HSF-TF.A.4)

**Standard**: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. (CCSS.Math.Content.HSF-TF.B.5)

**Standard**: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. (CCSS.Math.Content.HSF-TF.B.6)

**Standard**: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. (CCSS.Math.Content.HSF-TF.B.7)

**Standard**: Prove the Pythagorean identity sin2(theta) + cos2(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle. (CCSS.Math.Content.HSF-TF.C.8)

**Standard**: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. (CCSS.Math.Content.HSF-TF.C.9 )

## About This Chapter

Once students fully understand trigonometric functions, they'll be able to graph logarithmic and trigonometric functions and identify the different parts of those graphs. They'll also be able to find the sum of sine, tangent and cosine. Mastering the standard allows students to prove formulas and use the Pythagorean identity to find an angle's quadrant.

Lesson topics for this standard include:

- Introduction to sines, cosines and tangents
- Memorizing the first quadrant
- Converting between radians and degrees
- Special triangles and the unit circle
- Trigonometric functions, amplitude and periodicity
- Inverses of trigonometric functions
- List of the basic trigonometric equations

You'll know when students have mastered trigonometric functions when they're able to solve problems using addition and subtraction formulas, use the Pythagorean identity and graph the sine, cosine and tangent. They'll also understand the uses for the unit circle in solving trigonometric functions. Learning these concepts can help them with careers in such areas as navigation, construction and geology.

### How to Use These Lessons in Your Classroom

#### Assign Lessons as Homework

Since there are so many topics to cover in this lesson, you can assign some of them as homework and give students quizzes at the beginning of the next class. You might also want to set aside time for students to ask questions about anything that gave them trouble in the lesson, so they'll have a complete understanding in the lesson.

#### Let Students Write a Story

Some students might learn easier with words than they do numbers. Let students write a short story related to trigonometric functions, using unit circles, tangents, the Pythagorean identity and formulas as characters. This will give students a new perspective on the information they're learning and could prove as a more effective way for them to absorb the lesson.

#### Connect Sine, Cosine and Tangent

Since sine, cosine and tangent appear more than once in this lesson, you might want to group those lessons together so that students are able to make connections between identifying, graphing and using formulas for sine, cosine and tangent. Students might have an easier time connecting trigonometric functions with sine, cosine and tangent if they learn the related lessons all together.

### 1. Trigonometry: Sine and Cosine

Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.

### 2. Unit Circle: Memorizing the First Quadrant

Memorizing the unit circle can be a daunting task, but this lesson will show you a pattern to help you memorize the points, degree measures, and radian measures for the entire first quadrant.

### 3. Converting Between Radians and Degrees

Angles can be measured in degrees or radians. This lesson will explore the difference and provide you with a simple calculation that can be used to convert degrees into radians and radians into degrees.

### 4. List of the Basic Trig Identities

There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.

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### Other Chapters

Other chapters within the Common Core Math - Functions: High School Standards course

- Common Core HS Functions - Basics
- Common Core HS Functions - Sequences
- Common Core HS Functions - Graphing
- Common Core HS Functions - Linear Functions
- Common Core HS Functions - Quadratic Functions
- Common Core HS Functions - Common Functions & Transformations
- Common Core HS Functions - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Exponential & Logarithmic Functions