Class Units for Trigonometry

Last Updated: December 28, 2011

Trigonometry
Units
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Course Review
Chapter 7
Trigonometric Functions
  
Angles, Arcs, and Sectors
7.1Measurement of Angles
Objective: To find the measure of an angle in either degrees or radians and to find coterminal angles
7.2Sectors of Circles
Objective: To find the arc length and area of a sector of a circle and to solve problems involving apparent size.
The Trigonometric Functions
7.3The Sine and Cosine Functions
Objective: To use the definition of sine and cosine to find values of these functions and to solve simple trigonometric equations.
7.4Evaluating and Graphing Sine and Cosine
Objective: To use reference angles, calculators or tables, and special angles to find values of the sine and cosine functions and to sketch the graphs of these functions.
7.5The Other Trigonometric Functions
Objective: To find the tangent, cotangent, secant, and cosecant functions and to sketch the functions’ graphs.
7.6The Inverse Trigonometric Functions
objective: To find values of the inverse trigonometric functions.
Chapter 7 Essential Questions
 How is trigonometry used to find unknown values?
 Why are certain values undefined for certain functions?
 How can you compare the graphs of the sine, cosine, tangent functions and their inverses?
Key Concepts/Vocabulary
Concept:1. apparent size
Concept:2. arc, arc length
Concept:3. central angle
Concept:4. circumference
Concept:5. cosine, , cotangent
Concept:6. coterminal
Concept:7. degree, minute, second
Concept:8. initial ray
Concept:9. inverse functions
Concept:10.line
Concept:11.pi
Concept:12.quadrantal angle
Concept:13.radian, radian measure, radius
Concept:14.ray
Concept:15.reference angles
Concept:16.revolution
Concept:17.secant, cosecant
Concept:18.sector, area of a sector
Concept:19.sine, cosine
Concept:20.tangent
Concept:21.terminal ray
Concept:22.trigonometry
Content Covered
Text Book
Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • Chapter 7

Online Resouces

Trigonometric Functions

Summary and Reminders
    Summary

    Reminders
Student Handouts/Resources
 

Trigonometry
Units
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Course Review
Chapter 8
Trigonometric Equations and Applications
  
Equations and Applications of Sine Waves
8.1Simple Trigonometric Equations
Objective: To solve simple trigonometric equations and to apply them.
8.2Sine and Cosine Curves
Objective: To find equations of different sine and cosine curves and to apply these equations.
8.3Modeling Periodic Behavior
Objective: To use trigonometric functions to model periodic behavior.
Identities and Equations
8.4Relationships Among the Functions
Objective: To simplify trigonometric expressions and to prove trigonometric identities.
8.5Solving More Difficult Trigonometric Equations
Objective: To use trigonometric identities or technology to solve more difficult trigonometric equations.
Chapter 8 Essential Questions
 What approaches can be used to verify an identity?
 What is the best approach that can be used to verify an identity?
Key Concepts
Concept:1. amplitude
Concept:2.axis
Concept:3.cofunctions
Concept:4. conic section
Concept:5. direction angle
Concept:6. frequency
Concept:7. horizontal shift, vertical shift
Concept:8. inclination of a line
Concept:9. period of a function, periodic behavior
Concept:10. pythagorean relationships
Concept:11. trigonometric equations
Concept:12.trigonometric identities
Content Covered
Text Book
Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • Chapter 8, “Overview of C,” pp. 70-100, Section 2.5 through Chapter Review

Online Resources

Analytic Trigonometry

Summary and Reminders
    Summary

    Reminders
Student Handouts/Resources
 
    Chapter 8

Trigonometry
Units
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Course Review
Chapter 9:
Triangle Trigonometry
  
Chapter 9 Sections and Objectives
9.1Solving Right Triangles
Objective: To use trigonometry to find unknown sides or angles of a right triangle.
9.2The Area of a Triangle
Objective: To find the area of a triangle given the length of two sides and the measure of the included angle.
9.3The Law of Sines
Objective: To use the Law of Sines to find unknown parts of triangles.
9.4The Law of Cosines
Objective: To use the law of cosines to find unknown parts of a triangle.
9.5Applications of Trigonometry to Navigation and Surveying
Objective:To use trigonometry to solve navigation and surveying problems.
Chapter 9 Essential Questions
 How can you determine if a triangle had no solution, one solution, or two solutions?
How can you solve triangles using these laws?
  Why can’t physical models of vector quantities be represented by scalar quantities?
Key Concepts
Concept:1. Solving a triangle
Concept:2.Area of a triangle
Concept:3.A segment of a circle
Concept:4. The Law of Sines
Concept:5. The Law of Cosines
Concept:6. Course, compass bearing
Content Covered
Text Book
Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • Chapter 9

Online Resouces

Summary and Reminders
    Summary

    Reminders
Student Handouts/Resources
 
    Chapter 9

Trigonometry
Units
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Course Review
Chapter 10
Trigonometric Addition Formulas
  
Chapter 10 Sections and Objectives
10.1Formulas for cos() and sine()
Objective: To derive and apply formulas for cos() and sine().
10.2Formulas for tan()
Objective:To derive and apply formulas for tan().
10.3Double-Angle and Half Angle Formulas
Objective: To derive and apply double-angle and half-angle formulas.
10.4Solving Trigonometric Equations
Objective: To use identities to solve trigonometric equations.
Chapter 10 Essential Questions
 How can using trigonometric identities help us to solve trigonometric equations?
Key Concepts
Concept:1. sum, difference, double-angle, half-angle formulas
Concept:2.Solving trigonometric equations
Content Covered
Text Book
Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • Chapter 10

Online Resources

Summary and Reminders
    Summary

    Reminders
Student Handouts/Resources
 
    Chapter 10

Trigonometry
Units
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Course Review
Chapter 11
Polar Coordinates and Complex Numbers
  
Chapter 11 Sections and Objectives
11.1Polar Coordinates and Graphs
Objective: To graph polar equations
11.2Geometric Representation of Complex Numbers
Objective: To write complex numbers in polar form and to find products in polar form.
11.3Powers of Complex Numbers
Objective: To use De Moivre’s theorem to find powers of complex numbers.
11.4Roots of Complex Numbers
Objective: To find roots of complex numbers.
Chapter 11 Essential Questions
 Why is it important to understand complex numbers?
Key Concepts/Vocabulary
Concept:1. Imaginary units
Concept:2.Complex number
Concept:3.Standard form of complex numbers(Trigonometric form of a complex number)
Concept:4. Complex conjugate
Concept:5. Polar coordinate system
Concept:6. Polar axis
Concept:7. DeMoivre’s theorem
Concept:8. Nth root of a complex number
Concept:9. Conjugate pairs
Content Covered
Text Book
Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • Chapter 11

Online Resouces

    Online Videos

Homework  
Summary and Reminders
    Summary

    Reminders
Student Handouts/Resources
  No handouts at this time

Trigonometry
Units
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Course Review
Course Review and Semester Exam
  
Upon successful completion of this course, the student will be able to:
1. express an angle measure in radians, or Degrees, Minutes, Seconds, or Decimal Degrees;
convert degrees to radians and radians to degrees.
2. determine an angle coterminal with a given angle.
3. use the properties of similar triangles to determine missing sides or angles.
4. demonstrate and applly the definitions of the trigonometric functions.
5. demonstrate and apply the reciprocal, Pythagorean, and quotient identities.
6. use the definition of trigonometric ratios to solve a right triangle problem.
7. determine the trigonometric ratios of special angles given in radian measure.
8. state and apply the formula to determine the length of an arc; state and apply the formula to determine the area of a sector.
9. create a graph of the trigonometric functions
10.identify a sine or cosine function, given its amplitude, period, and phase shift.
11.demonstrate and apply the fundamental identities.
12.evaluate an expression involving trigonometric functions and inverse trigonometric functions
13.solve a trigonometric equation involving multiple of halfangles;
solve an equation involving inverse trigonometric functions.
Content Covered
Text Book
Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • See sections as specified for each Unit.

Online Resouces

Many references will be provided throughout the course.

Student Handouts/Resources
 
    Sample Semester Exam Questions
  • Part I - questions not yet available
  • Part II
  • Part III - questions not yet available