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MA003: Precalculus II

Unit 1: Trigonometric Functions of Angles  

Imagine standing some distance from a building and trying to guess at its height. With some simple measurements and the tools you learn in this unit, you will be able to find the height of the building precisely. This is one of the many application problems you will be able to solve after your study of trigonometry. 

In this unit, you will explore the properties of circles and use those properties to investigate angles within the circle. In particular, you will begin with a new definition of angle measure related to arc length in a circle. A review of the equation for a circle with radius r leads to a definition of the sine and cosine functions, and you will use these to define the remaining trigonometric functions and explore their basic properties and identities. These definitions will be used to derive similar definitions for right triangle trigonometry, which is precisely the tool needed to solve problems like the one mentioned above.

Unit 1 Time Advisory
This unit should take you approximately 17 hours to complete.

☐    Subunit 1.1: 2 hours

☐    Subunit 1.2: 4 hours

☐    Readings: 2 hours

☐    Assignments: 1.5 hours

☐    Assessments: 0.5 hours

☐    Subunit 1.3: 3 hours

☐    Subunit 1.4: 3.25 hours

☐    Subunit 1.5: 2.25 hours

☐    Unit 1 Assignment (Review): 1 hour

☐    Unit 1 Assessment: 1.5 hours

Unit1 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

  • convert radians to degrees and vice versa;
  • solve applied problems involving arc length and linear/angular speed;
  • calculate the reference angle for a given angle and compute or determine angles coterminal with a given angle;
  • apply the definitions of the trigonometric functions in terms of right triangles to solve for missing sides and angles of right triangles;
  • apply the definitions of the trigonometric functions in terms of the unit circle to state the coordinates of a point on a circle in terms of sine and cosine;
  • given a trigonometric function value for an angle (real number), determine the other five trigonometric function values for the same angle (real number);
  • solve applied problems involving right triangle trigonometry;
  • determine or calculate trigonometric function values for π/6, π/4, π/3, π/2, and π as well as angles that are coterminal to these or have these as reference angles without outside reference or calculator; and
  • prove trigonometric identities that require multiple steps and algebraic and trigonometric manipulation.

1.1 Circles   - Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions” Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions (PDF)
 
Instructions: Read pages 297-301 of Chapter 5 to learn about circles in trigonometry. Note that this reading covers the material in subunits 1.1.1 through 1.1.4.

Terms of Use: The article above is released under a [Creative
Commons Attribution-Share-Alike License
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attributed to Lippman & Rasmussen.

1.1.1 The Pythagorean Theorem   Note: This topic is covered in the reading under subunit 1.1. To learn about the Pythagorean Theorem focus on the material on page 297.

1.1.2 The Distance Formula   Note: This topic is covered in the reading under subunit 1.1. To learn about the Distance Formula, focus on the material on pages 297 and 298. Pay particular attention to the examples in the text, and work the “Try It Now” problems; solutions are available at the end of each section of reading.

  • Web Media: YouTube: Math Warehouse’s “Distance Formula- Tutorial, Practice Problems, and Other Goodies” Link: YouTube: Math Warehouse’s “Distance Formula- Tutorial, Practice Problems, and Other Goodies” (YouTube)
     
    Instructions: Watch this video for a comprehensive overview of the distance formula.

    Watching this video should take approximately 10 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.1.3 Equation of a Circle   Note: This topic is covered by the reading under subunit 1.1. Focus on the material on pages 298 and 299 to learn about the equation of a circle. Pay particular attention to the examples in the text, and work the “Try It Now” problems; solutions are available at the end of each section of reading.

  • Web Media: YouTube: Brightstorm’s “Equation of a Circle” Link: YouTube: Brightstorm’s “Equation of a Circle” (YouTube)
     
    Instructions: Watch this video for a better understanding of writing the equation of a circle.

    Watching this video should take approximately 3 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.1.4 Points on a Circle   Note: Points on a circle is one of the topics included in the reading listed under subunit 1.1. Pay particular attention to pages 300 and 301 and to the examples in the text. Work through the “Try It Now” problems; solutions are available at the end of each section of reading.

  • Web Media: YouTube: Mathew Mattakad’s “Finding Points of Intersection between a Line and a Circle” Link: YouTube: Mathew Mattakad’s “Finding Points of Intersection between a Line and a Circle” (YouTube)
     
    Instructions: Watch this video and work through the examples discussed within. Then use what you have learned to re-do any problems that you had difficulty with before.
     
    Watching this video should take approximately 15 minutes.
     
    Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Mathew Mattakad, and the original version can be found here.

  • Assessment: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.1: Circles Graded Homework” Link: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.1: Circles Graded Homework” (HTML)

    Instructions: Once you have completed the readings and viewed the material for all of subunit 1.1, complete this assessment. You will need to create a free account in order to access the material. If you have already created an account, log in to access the assessment. Your answers will be scored upon submission. 

1.2 Angles   - Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions” Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions (PDF)
 
Instructions: Read pages 307-317 of Chapter 5 to learn about angles in trigonometry. Pay particular attention to the new form of angle measure, the radian.  A complete grasp of this concept will serve you well through the remainder of the course. Also note that this reading covers the material in subunits 1.2.1 through 1.2.5.

Terms of Use: The article above is released under a [<span
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It is attributed to Lippman & Rasmussen.

1.2.1 Measuring Angles   Note: This topic is covered by the reading listed under subunit 1.2. Focus on page 307 to master measuring angles. 

1.2.2 Working with Angles in Degrees   Note: This topic is covered by the reading listed under subunit 1.2. Read pages 308 and 309, and be sure to work through the examples for finding coterminal angles before you move on. Pay particular attention to the examples in the text, and work the “Try It Now” problems; solutions are available at the end of each section of reading.

  • Web Media: YouTube: patrickJMT’s “Coterminal Angles - Example 3” Link: YouTube: patrickJMT’s “Coterminal Angles - Example 3” (YouTube)
     
    Instructions: This video provides further examples of finding coterminal angles. Watch it and re-work problems from the reading that you found difficult.

    Watching this video should take approximately 3 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

  • Web Media: YouTube: clindelof’s “How to Find Coterminal Angles (Positive and Negative) Degrees: Precalculus” Link: YouTube: clindelof’s “How to Find Coterminal Angles (Positive and Negative) Degrees: Precalculus (YouTube)

                                                                                                                         
    Instructions: This video provides further examples of finding coterminal angles. Watch it and re-work problems from the reading that you found difficult.

    Watching this video should take approximately 6 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.3 Angles in Radians   Note: This topic is covered by the reading listed under subunit 1.2. Pages 309-313 focus on angles in radians. A thorough understanding of the definition of a radian as well as the conversion between radians and degrees is important to your success in this course. Pay particular attention to the examples in the text, and work the “Try It Now” problems; solutions are available at the end of each section of reading. 

  • Web Media: YouTube: eHow’s “Mathematics: Geometry & Trigonometry: How to Convert Degrees to Radians” Link: YouTube: eHow’s “Mathematics: Geometry & Trigonometry: How to Convert Degrees to Radians (YouTube)
     
    Instructions: This video reviews the concept of radian/degree conversion. Watch the brief video clip and re-work any problems in the chapter that you had difficulty with.

    Watching this video should take approximately 1 minute.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: AcademicLeadersEd’s “Conversion of Radians to Degrees and Vice-versa (Easy!)” Link: YouTube: AcademicLeadersEd’s “Conversion of Radians to Degrees and Vice-versa (Easy!)” (YouTube)

    Instructions: This brief video reviews the concept of radian/degree conversion. Watch the video clip and re-work any problems in the chapter that you had difficulties with.

    Watching this video should take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above. 

  • Web Media: YouTube: American Public University System’s “Radian Measure of Coterminal Angles” Link: YouTube: American Public University System’s “Radian Measure of Coterminal Angles (YouTube)
     
    Instructions: This video reviews the concept of radian/degree conversion and revisits the earlier topic of coterminal angles. Watch the video and re-work any problems in the chapter that you had difficulty with.
     
    Watching this video should take approximately 5 minutes. 

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.2.4 Arclength and Area of a Sector   Note: This section is covered in the reading under subunit 1.2. Read the material on pages 298 and 299 to learn about arclength and area of a sector, and work through the exercises. Complete the “Try It Now” exercises; solutions are available at the end of each section of reading.

  • Web Media: YouTube: Mindbites.com’s “Trig: Radians, Arc Length, Solve 1st Deg Equations” Link: YouTube: Mindbites.com’s “Trig: Radians, Arc Length, Solve 1st Deg Equations (YouTube)
     
    Instructions: This video provides further instruction for computing arc lengths. Watch the video and re-work any problems you had difficulty with in the readings.

    Watching this video should take approximately 6 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: Mr. Pilarski’s “Arc Length Theorem: How to Find the Length of an Arc” Link: YouTube: Mr. Pilarski’s “Arc Length Theorem: How to Find the Length of an Arc (YouTube)
     
    Instructions: This video provides further instruction for computing arc lengths. Watch the video and re-work any problems you had difficulty with in the readings.

    Watching this video should take approximately 6 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: Tucson Math Doc’s “How to Find Arc Length? (Shortcut!)” Link: YouTube: Tucson Math Doc’s “How to Find Arc Length? (Shortcut!)” (YouTube)
     
    Instructions: This video provides further instruction for computing arc lengths. Watch the video and re-work any problems you had difficulty with in the readings.

    Watching this video should take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above. 

  • Web Media: YouTube: BabelMath’s “Area of a Sector” Link: YouTube: BabelMath’s “Area of a Sector” (YouTube)

    Instructions: This video provides further instruction for computing the area of a sector. Watch the video and re-work any problems you had difficulty with in the readings.

    Watching this video should take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.2.5 Linear and Angular Velocity   Note: Linear and angular velocity is covered in the reading for subunit 1.2. Pay careful attention to pages 315-317, and be sure to work through all the examples. Make sure you attempt the “Try It Now” problems; solutions for these are found at the end of the section of reading.

  • Web Media: YouTube: 123MrBee’s “Angular Velocity Speed Word Problem: Trigonometry Math Help” Link: YouTube: 123MrBee’s “Angular Velocity Speed Word Problem: Trigonometry Math Help (YouTube)
     
    Instructions: Watch this video for a better understanding of angular velocity.

    Watching this video should take approximately 6 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

  • Activity: Washington State Board for Community and Technical Colleges’ “Music Listening Technology” Worksheet Link: Washington State Board for Community and Technical Colleges’ “Music Listening Technology” Worksheet (PDF)
     
    Instructions: Changes in the technology for reproducing music provide an interesting context for studying circular speeds. Complete the worksheet by reading the text and answering all 6 questions to study the differences between linear and angular velocities for CD’s and records.

  • Assessment: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.2: Angles Graded Homework” Link: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.2: Angles Graded Homework (HTML)

    Instructions: Once you have completed the readings and viewed the material for all of subunit 1.2, complete this assessment. You will need to create a free account in order to access the material. If you have already created an account, log in to access the assessment. Your answers will be scored upon submission. 

  • Assessment: Washington State Board for Community and Technical Colleges’ “Chapter 5 Quiz 1” Link: Washington State Board for Community and Technical Colleges’ “Chapter 5 Quiz 1” (PDF)
     
    Instructions: This assessment covers subunits 1.1.and 1.2. Complete this quiz after you have worked through the readings, web media, and assignments for subunits 1.1 and 1.2.

1.3 Points on Circles Using Sine and Cosine   - Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions” Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions” (PDF)
 
Instructions: Read pages 321-330 of Chapter 5 to learn points on circles using sine and cosine. The unit circle is one of the key concepts in trigonometry, and a complete understanding how the coordinates from the equation of the circle are used to create the trig functions is fundamental to understanding the derivations of the graphs of the functions and all the useful identities we will study in later sections. Committing the unit circle to memory is a useful skill. This reading covers the material in subunits 1.3.1 through 1.3.4.

Terms of Use: The article above is released under a [Creative
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attributed to Lippman & Rasmussen.

1.3.1 The Sine and Cosine Functions   Note: This section is covered by the reading listed under subunit 1.3. Pay attention to the readings on pages 321-323 and in particular the relationship between the terminal points of an angle on the unit circle and its sine and cosine.

  • Web Media: YouTube: sgordo3398’s “Section 5.3 #1” Link: YouTube: sgordo3398’s “Section 5.3 #1” (YouTube)
     
    Instructions: This video is optional for the student, but may provide particular insight into some of the assigned problems for subunit 1.3.

    Watching this video should take approximately 2 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.3.2 Pythagorean Identity   Note: Note that this topic is covered by the reading listed under subunit 1.3. Pay attention to the information on page 323 to understand how the Pythagorean Identity follows naturally from the equation of the unit circle. As always, work through examples and “Try It Now” problems; solutions to the Try It Now problems are available at the end of the reading section.

1.3.3 Unit Circle Values   Note: Note that this topic is covered by the reading listed under subunit 1.3. There are several important values for the sine and cosine functions on the unit circle. Read pages 324-327 and begin to commit these values to memory. Be sure to work the “Try It Now” problems and go over the example problems. Solutions to the Try It Now problems appear at the end of the reading selection.

  • Web Media: YouTube: sgordo3398’s “Section 5.3 #2” Link: YouTube: sgordo3398’s “Section 5.3 #2 (YouTube)

    Instructions: This optional video may prove useful in solving the exercises in the assignment for subunit 1.3.

    Watching this video should take approximately 2 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above. 

  • Web Media: YouTube: 123MrBee’s “How to Find a Point on the Unit Circle Pt1: Trigonometry Math Help” Link: YouTube: 123MrBee’s “How to Find a Point on the Unit Circle Pt1: Trigonometry Math Help” (YouTube)
     
    Instructions: Watch this video to clarify your understanding of the unit circle, and rework the exercises or “Try It Now” problems you had difficulty with.

    Watching this video should take approximately 7 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.3.4 Reference Angles   Note: This section gives a discussion on using reference angles to determine the sine or cosine of an angle of any measure. It is covered by the reading listed under subunit 1.3; pay attention to pages 327-330, working through the examples and completing the “Try It Now” problems. Solutions to these problems appear at the end of the reading section.

  • Web Media: Brightstorm’s “Evaluating Cosine” Link: Brightstorm’s “Evaluating Cosine (Flash Video)       
     
    Instructions: View this video and use the information in it to deepen your understanding of the reading.

    Watching this video will take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: speakerbill’s “Reference Angles Introduction” Link: YouTube: speakerbill’s “Reference Angles Introduction (YouTube)
     
    Instructions: After watching this video be sure to re-work the examples in the text that you previously had difficulty with.

    Watching this video should take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: Khan Academy’s “The Unit Circle Definition of Trigonometric Function” Link: YouTube: Khan Academy’s “The Unit Circle Definition of Trigonometric Function” (YouTube)
     
    Instructions: After watching this video be sure to re-work the examples in the text that you previously had difficulty with.

    Watching this video should take approximately 10 minutes.

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

  • Web Media: YouTube: sgordo3398’s “Section 5.3 #7,” “Section 5.3 #9” and “Section 5.3 #10” Links: YouTube: sgordo3398’s “Section 5.3 #7,” “Section 5.3 #9,” and “Section 5.3 #10 (YouTube)
     
    Instructions: These videos relate to specific problems in the assignment for subunit 1.3 and will help you understand how to complete problems 7, 9, and 10 in this assignment.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  

  • Assessment: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.3: Points on Circles using Sine and Cosine Graded Homework” Link: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.3: Points on Circles using Sine and Cosine Graded Homework (HTML)

    Instructions: Once you have completed the readings and viewed the material for all of subunit 1.3, complete this assessment. Your answers will be scored upon submission. 

  • Assessment: Washington State Board for Community and Technical Colleges’ “Chapter 5 Quiz 2” Link: Washington State Board for Community and Technical Colleges’ “Chapter 5 Quiz 2” (PDF)

    Instructions: This quiz uses the information from subunit 1.3 as well as in the previous sections. Complete it after you have worked through the material in this subunit.  

1.4 The Other Trigonometric Functions   - Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions” Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions (PDF)
 
Instructions: Read pages 333-338 of Chapter 5 to learn about the other trigonometric functions and some important identities, establishing some relationships between all six of the trigonometric functions. This reading covers the material in subunits 1.4.1 through 1.4.3.

Terms of Use: The article above is released under a [Creative
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attributed to Lippman & Rasmussen.

1.4.1 Tangent, Secant, Cosecant, and Cotangent Functions   Note: The reading for this topic is contained in the reading for subunit 1.4. Pay attention to page 333 to develop an understanding of the four additional trig functions as ratios of the sine and cosine. As always, work through the examples on your own and complete the ‘Try It Now” problems, and check your solutions at the end of the selected reading.

  • Web Media: Brightstorm’s “Reciprocal Trigonometric Functions” Link: Brightstorm’s “Reciprocal Trigonometric Functions (Flash Video)
     
    Instructions: Watch this video to deepen your understanding of the tangent, cotangent, secant, and cosecant as reciprocals of sine and cosine.

    Watching this video should take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: sgordo3398’s “Section 5.4 #4” Link: YouTube: sgordo3398’s “Section 5.4 #4 (YouTube)

    Instructions: Watch this video; it will be particularly useful when you complete the assignment at the end of the subunit.

    Watching this video should take approximately 2 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: bullcleo1’s “Determining Trigonometric Function Values on a Calculator” Link: YouTube: bullcleo1’s “Determining Trigonometric Function Values on a Calculator (YouTube)
     
    Instructions: Watch this video to learn how to accurately compute values of the trig functions using a calculator. There are numerous pitfalls in these calculations; the video can help you avoid them.

    Watching this video should take approximately 6 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.4.2 Some Important Trig Identities   Note: This topic is covered by the reading under subunit 1.4. Focus on the information on pages 333-337 for some additional important trig functions. Be sure to work through the example problems yourself and attempt the “Try It Now” problems. 

  • Web Media: YouTube: MrEmrah57’s “11 2 Simplifying Trig Expressions” Link: YouTube: MrEmrah57’s “11 2 Simplifying Trig Expressions (YouTube)
     
    Instructions: Watch this video to get further insight into using the trig identities you have learned thus far to simplify trigonometric expressions. 

    Watching this video should take approximately 6 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: Brightstorm’s “Precalculus-Using Trigonometric Identities” Link: YouTube: Brightstorm’s “Precalculus-Using Trigonometric Identities (YouTube)
     
    Instructions: Watch this video to get further insight into using the trig identities you have learned thus far to simplify trigonometric expressions.

    Watching this video should take approximately 3 minutes. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above. 

1.4.3 Alternate Forms of the Pythagorean Identity   Note: There are several forms of the Pythagorean Identity that use the new reciprocal trig functions. The reading listed under subunit 1.4 covers these on pages 337 and 338. Pay attention to the examples in the text and work through the “Try It Now” problems. Solutions to these problems are available at the end of the selected reading.

  • Web Media: YouTube: Mindbites.com’s “Trigonometry: Simplify Fractional Trig Expression” Link: YouTube: Mindbites.com’s “Trigonometry: Simplify Fractional Trig Expression (YouTube)
     
    Instructions: Watch this video and rework and problems you had with the examples on pages 337 and 338.

    Watching this video should take approximately 3 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above. 

  • Web Media: YouTube: patrickJMT’s “Simplifying Trigonometric Expressions Using Identities, Example 1” Link: YouTube: patrickJMT’s “Simplifying Trigonometric Expressions Using Identities, Example 1 (YouTube)
     
    Instructions: Watch this video to reinforce your understanding of the use of identities to simplify trig expressions.

    Watching this video should take approximately 1 minute.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Washington State Board for Community and Technical Colleges’ “Classwork- Identities” Worksheet Link: Washington State Board for Community and Technical Colleges’ “Classwork- Identities” Worksheet (PDF)
     
    Instructions: Complete this identity worksheet for additional practice using the identities in subunit 1.4 

  • Assessment: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.4 The Other Trig Functions Graded Homework” Link: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.4 The Other Trig Functions Graded Homework” (HTML)

    Instructions: Once you have completed the readings and viewed the material for all of subunit 1.4, complete this assessment. You will need to create a free account in order to access the material. If you have already created an account, log in to access the assessment. Your answers will be scored upon submission. 

  • Assessment: Washington State Board for Community and Technical Colleges’ “Chapter 5 Quiz 3” Link: Washington State Board for Community and Technical Colleges’ “Chapter 5 Quiz 3 (PDF)
     
    Instructions: This quiz uses the information from subunit 1.4 as well as in the previous sections. Complete it after you have worked through the material in this subunit. 

1.5 Right Triangle Trigonometry   - Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions” Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 5: Trigonometric Angles of Functions (PDF)
 
Instructions: Read pages 343-347 of Chapter 5 to learn about the trig functions in the context of right triangles. Note that this reading covers subunits 1.5.1 through 1.5.3. 

 Terms of Use: The article above is released under a [Creative
Commons Attribution-Share-Alike License
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attributed to Lippman & Rasmussen.

1.5.1 Right Triangle Relationships with Sine, Cosine, and Tangent   Note: This topic is covered in the reading listed under subunit 1.5. Focus on the content of pages 343 and 344, paying particular attention to the worked examples, and completing any “Try It Now” problems in the text. The solutions to these problems are located at the end of the selected reading.

  • Web Media: YouTube: Mindbites.com’s “Pre-Calculus: Fundamental Trigonometric Identities” Link: YouTube: Mindbites.com’s “Pre-Calculus: Fundamental Trigonometric Identities (YouTube)
     
    Instructions: Watch this video to review right triangle trigonometry. 

    Watching this video should take approximately 4 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: YourTeacher.com’s “Sin Cos Tan—Basic Trigonometry” Link: YouTube: YourTeacher.com’s “Sin Cos Tan—Basic Trigonometry (YouTube)
     
    Instructions: Watch this video to review right triangle trigonometry. Rework any examples or problems you previously had difficulty with.

    Watching this video should take approximately 4 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

1.5.2 The Cofunction Identities   Note: This topic is covered by the reading under subunit 1.5. Focus on page 345 to learn about the cofunction identities, and be sure to work through the practice problems.  

1.5.3 Right Triangle Trig Applications   Note: This topic is covered by the reading under subunit 1.5. Focus on pages 345-347. Work through the examples and “Try It Now” problems to get a working knowledge of the applications of right triangle trigonometry. The solutions to these are available at the end of the selected reading.

  • Web Media: YouTube: Mindbites.com’s “Trig: Word Problems—Sine, Cosine & Tangent” Link: YouTube: Mindbites.com’s “Trig: Word Problems—Sine, Cosine & Tangent (YouTube)
     
    Instructions: Watch the video, trying any problems on your own and checking the video for accuracy.

    Watching this video should take approximately 4 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

  • Web Media: YouTube: patrickJMT’s “Trigonometry Word Problem, Finding the Height of a Building, Example 1” Link: YouTube: patrickJMT’s “Trigonometry Word Problem, Finding the Height of a Building, Example 1 (YouTube)
     
    Instructions: Watch the video, trying any problems on your own and checking the video for accuracy.

    Watching this video should take approximately 8 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: Brightstorm’s “Angle of Elevation and Depression” Link: YouTube: Brightstorm’s “Angle of Elevation and Depression (YouTube)
     
    Instructions: Watch the video, trying any problems on your own and checking the video for accuracy.

    Watching this video should take approximately 2 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.   

  • Web Media: YouTube: sgordo3398’s “Section 5.5 #7” Link: YouTube: sgordo3398’s “Section 5.5 #7” (YouTube)
     
    Instructions: This optional video will be useful to solve the problems in the assignment at the end of the subunit.

    Watching this video should take approximately 2 minutes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.5 Graded Homework” Link: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Section 5.5 Graded Homework (HTML)

    Instructions: Once you have completed the readings and viewed the material for all of subunit 1.4, complete this assessment. You will need to create a free account in order to access the material. If you have already created an account, log in to access the assessment. Your answers will be scored upon submission. 

  • Assessment: Washington State Board of Community and Technical Colleges’ “Chapter 5 Quiz 4” Link: Washington State Board of Community and Technical Colleges’ “Chapter 5 Quiz 4 (PDF)
     
    Instructions: This quiz uses the information from Subunit 1.5 as well as in the previous sections. Complete it after you have worked through the material in this subunit.

Unit 1 Review   - Assessment: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Chapter 5 Review” Link: Washington State Board for Community and Technical Colleges’ MyOpenMath: “Chapter 5 Review (HTML)

 Instructions: Once you have completed the readings and viewed the
material for all of unit 1, complete this assessment. You will need
to create a free account in order to access the material. If you
have already created an account, log in to access the assessment.
Your answers will be scored upon submission. This will provide a
review for your unit assessment.

Unit 1 Assessment   - Assessment: Washington State Board for Community and Technical Colleges’ “Chapter 5 Exam 1a” Link: Washington State Board for Community and Technical Colleges’ “Chapter 5 Exam 1a” (PDF)
 
Instructions: Complete this assessment when you have completed all of the material in Unit 1. You should complete the assessment without the use of a calculator.