## Overview

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*This course is a credit-bearing Precalculus Mathematics.*

** MyMathLab for Reasoning with Functions II **is part of a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center’s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways.

* *

*Reasoning with*** Functions II **is designed for students who have completed Reasoning with Functions I and intend to take Calculus or STEM coursework that requires a thorough knowledge of functions and algebraic reasoning. Reasoning with Functions II builds students' geometric and trigonometric reasoning skills, providing opportunities to explore dynamic geometric situations as well as build and use mathematical models that incorporate trigonometric functions. The MyMathLab course designed to be used with Reasoning with Functions II provides:

- Interactive content to help prepare students for active classroom time
- In-Class Interactive Lessons to support students through an active classroom experience, accompanied by notebook PDFs
- Homework assignments designed to assess conceptual understanding of important skills and concepts
- Additional resources for instructors to help facilitate an interactive and engaging classroom

**Built in MyMathLab**

Content developed by the Charles A. Dana Center at The University of Texas at Austin will be delivered through MyMathLab. MyMathLab is an online homework, tutorial, and assessment program that engages students and improves results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

## Table of contents

**Lesson 1: Area Under a Curve and an Introduction to Optimization**

1.A** — **Approximating Area

1.B — Optimization and Rectangles

1.C - Our Learning Community

**Lesson 2: Geometry of Triangles and the Pythagorean Theorem**

2.A — Geometry of Triangles: Area

2.B — Right Triangles and Rates

2.C - Distance and Arc Length

**Lesson 3: Rates of Change: Expanding Circles and Spheres**

3.A — Circles and Rates of Change

3.B — Spheres and Rates of Change

3.C - Forming Effective Study Groups

**Lesson 4: Equations of Circles**

4.A — Distance on the Line

4.B — Circles

4.C — Equations of Circles

**Lesson 5: Similar Triangles, Circular Motion, and Measuring Angles**

5.A — Moving Shadows

5.B — Home Improvement

5.C — You Spin Me Round

**Lesson 6: Related Rates and Optimization: Cones and Cylinders**

6.A — Red Plastic Cup

6.B — Can It!

6.C — Off to a Rocky Start

6.D — A Geometric Problem

**Lesson 7: Sinusoidal Models**

7.A — Modeling Tides

7.B — Pendulum Motion

7.C — Modeling Temperature Change

**Lesson 8: The Unit Circle**

8.A — Constructing Sinusoids From Circles

8.B — The Sine and Cosine Functions

8.C — Special Angles

8.D — Special Values of Sinusoidal Functions

**Lesson 9: Circles and Sinusoidal Models**

9.A — Non-Unit Circles

9.B — Changes in Angle and Radius

9.C — Damped Harmonic Motion

**Lesson 10: Analyzing Sinusoidal Functions**

10.A — Modeling the Motion of a Pendulum

10.B — Modeling Cell Phone Signals

10.C — Modeling the Vibration of a Cell Phone

**Lesson 11: Transformations of Sinusoidal Functions**

11.A — Staying Current Around the World

11.B — Periodic Models With Vertical Shifts

11.C — Periodic Models With Horizontal Shifts

**Lesson 12: Describing Change In Sinusoidal Functions**

12.A — Rate of Change of Sine

12.B — A Closer Look at Rate of Change of Sine

12.C — Applications of Rate of Change of Sine

12.D — Amplitude Decay of Sine Functions

**Lesson 13: Right Triangle Trigonometry**

13.A — From Circles to Triangles

13.B — From Circles to Triangles (Continued)

13.C — Hypotenuse Trouble

13.D — A Sine of Things to Come

**Lesson 14: Inverse Trigonometric Functions**

14.A — Does Inverse Cosine Exist?

14.B — Understanding the Inverse Cosine Function

14.C — Is this Ladder Safe?

**Lesson 15: Solving Trigonometric Equations**

15.A — Equations Involving Sine and Cosine

15.B — Solving for Obtuse Angles

15.C — Choosing the Quadrant

15.D — Solving Trigonometric Equations

**Lesson 16: The Pythagorean Identity and Polar Curves**

16.A — The Pythagorean Identity

16.B — Is My Answer Right?

16.C — Polar Graphs

16.D — A Gallery of Polar Curves

**Lesson 17: Sum and Difference Identities**

17.A — Angle Sum Identities

17.B — What’s the Difference?

17.C — Guitar Harmonics

17.D — In Tune

**Lesson 18: Double and Half-angle Formulas**

18.A — Projectile Motion

18.B — Malus’ Law

18.C — Planetary Motion

18.D — Circular Motion

**Lesson 19: Law of Sines and Law of Cosines**

19.A — The Montreal Tower

19.B — Can You Hear Me Now?

19.C — Play Ball!

19.D — Here Comes the Sun

19.E — Sines or Cosines?

** **

**Lesson 20: Secant and Tangent Functions**

20.A — The Tangent Function

20.B — Graphing the Tangent Function

20.C — The Inverse Tangent Function

20.D — The Secant Function

20.E — Identities Involving Secant and Tangent

**Lesson 21: Cosecant and Cotangent Functions**

21.A — The Cotangent Function

21.B — Inverting the Cotangent Function

21.C — The Cosecant Function

21.D — Inverses of Secant and Cosecant

**Lesson 22: Applications of Periodic Functions**

22.A — Rising Carbon Dioxide

22.B — Car Wheels

22.C — Train Wheels

22.D — Amplitude Modulation

** **

**Student Resources**

Overview

Angle Measure

Arithmetic with Fractions

Combining Like Terms

Coordinate Plane

Dimensional Analysis

Distributive Property

Exponent Rules

Factoring

Factoring Polynomials

Factoring Sums and Differences of Cubes

Four Representations of Functions

Geometry

Graphing Technology

Lines

Order of Operations

Parabolas and Quadratic Functions

Roots and Radicals

Scientific Notation

Slope

Solving Quadratic Equations

Transformations

Trigonometric Formulas

Writing Principles

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