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Course Question & AnswerReadings
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1.1 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.
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1.2 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.
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1.3 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.
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1.4 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.
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1.5 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.
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2.1 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions” (PDF)
Instructions: The graphs of the sinusoidal functions have some important features that help us construct them, and make them useful for modeling. Read pages 353-365 to gain an understanding of the properties of these graphs. This reading also covers the topics outlined in subunits 2.1.1 through 2.1.5.
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2.2 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions” (PDF)
Instructions: Much like the sinusoidal functions, the remaining trig function graphs have some key features that are important to understand. Read pages 369- 374 to understand these. This reading selection covers the topics outlined in subunits 2.2.1 through 2.2.4.
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2.3 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions” (PDF)
Instructions: The functions give us some powerful tools for equation solving. Read pages 379–384 to begin to understand them, their graphs, and their relationship to the trig functions. This reading covers the topics outlined in subunits 2.3.1 through 2.3.3.
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2.4 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions” (PDF)
Instructions: Now that you have an understanding of the inverse trig functions and the domains and ranges of both the trig and inverse trig functions, you can begin solving more complicated equations. Read pages 387-394 to understand how. This reading covers the topics outlined in subunits 2.4.1 and 2.4.2.
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2.5 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 6: Periodic Functions” (PDF)
Instructions: Trigonometry is very useful for modeling real world data. Read the selection on pages 397–403 to develop some modeling techniques. Note that this reading covers the topics outlined in subunits 2.5.1 and 2.5.2.
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3.1 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities” (PDF)
Instructions: Read pages 409–415 to learn some additional techniques for solving trig equations. This reading covers the topics outlined in subunits 3.1.1 and 3.1.2
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3.2 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities” (PDF)
Instructions: Add some additional identities to your problem solving arsenal by reading pages 417-430. This selection also covers the topics outlined in subunits 3.2.1–3.2.3.
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3.3 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities” (PDF)
Instructions: Read pages 431–441 to learn about simplifying trig expressions and solving trig equations involving double angles. This reading also covers the topics outlined in subunits 3.3.1 and 3.3.2.
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3.4 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 7: Trigonometric Equations and Identities” (PDF)
Instructions: Because real world phenomena are often modeled with trig functions, it is important to understand how changes to the functions affect the resulting graphs and the phenomena being modeled. To increase your understanding of this, read pages 442–448 of Chapter 7. This selection also covers the topics outlined in subunits 3.4.1 through 3.4.3.
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4.1 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry” (PDF)
Instructions: Pages 451–466 introduce the idea of using trigonometric functions in triangles other than right triangles. Read this selection carefully. This selection also covers the topics outlined in subunits 4.1.1 and 4.1.2.
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4.2 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry” (PDF)
Instructions: Read the selection from pages 467–475. The selection defines a new system for graphing points and curves based on distances and angles rather than the horizontal and vertical distances used in the Cartesian Coordinate system. This reading covers the topics outlined in subunits 4.2.1 through 4.2.3.
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4.3 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry” (PDF)
Instructions: Read pages 480–490 of Chapter 8 to learn how polar coordinates and complex numbers are related. This selection also covers the topics outlined in subunits 4.3.1 through 4.3.4.
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4.4 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry” (PDF)
Instructions: Vectors are geometric objects with both distance and direction, and they have numerous applications. Read pages 491-502 from Chapter 8 carefully to understand these applications. This reading selection also covers the topics outlined in subunits 4.4.1 through 4.4.3.
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4.5 Reading: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry”
Link: Lippman and Rasmussen’s Precalculus: An Investigation of Functions: “Chapter 8: Further Applications of Trigonometry” (PDF)
Instructions: Up until this point in the course, we have been defining functions in terms of two variables: a dependent and an independent variable. Parametric equations give us a new way to define functions, determining the coordinates of a point based on functions of a third variable, often time. Read pages 504–512 to learn about these concepts. This reading also covers the topics outlined for subunits 4.5.1 through 4.5.3.
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