About the Book
KEY BENEFIT 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.
KEY TOPICS Area Under a Curve and an Introduction to Optimization; Approximating Area; Optimization and Rectangles; Our Learning Community;
Geometry of Triangles and the Pythagorean Theorem; Geometry of Triangles: Area; Right Triangles and Rates; Distance and Arc Length;
Rates of Change: Expanding Circles and Spheres; Circles and Rates of Change; Spheres and Rates of Change; Forming Effective Study Groups;
Equations of Circles; Distance on the Line; Circles; Equations of Circles;
Similar Triangles, Circular Motion, and Measuring Angles; Moving Shadows; Home Improvement; You Spin Me Round;
Related Rates and Optimization: Cones and Cylinders; Red Plastic Cup; Can It!; Off to a Rocky Start; A Geometric Problem;
Sinusoidal Models; Modeling Tides; Pendulum Motion; Modeling Temperature Change;
The Unit Circle; Constructing Sinusoids From Circles; The Sine and Cosine Functions; Special Angles; Special Values of Sinusoidal Functions;
Circles and Sinusoidal Models; NonUnit Circles; Changes in Angle and Radius; Damped Harmonic Motion;
Analyzing Sinusoidal Functions; Modeling the Motion of a Pendulum; Modeling Cell Phone Signals; Modeling the Vibration of a Cell Phone;
Transformations of Sinusoidal Functions; Staying Current Around the World; Periodic Models With Vertical Shifts; Periodic Models With Horizontal Shifts;
Describing Change In Sinusoidal Functions; Rate of Change of Sine; A Closer Look at Rate of Change of Sine; Applications of Rate of Change of Sine; Amplitude Decay of Sine Functions;
Right Triangle Trigonometry; From Circles to Triangles; From Circles to Triangles (Continued); Hypotenuse Trouble; A Sine of Things to Come;
Inverse Trigonometric Functions; Does Inverse Cosine Exist?; Understanding the Inverse Cosine Function; Is this Ladder Safe?;
Solving Trigonometric Equations; Equations Involving Sine and Cosine; Solving for Obtuse Angles; Choosing the Quadrant; Solving Trigonometric Equations;
The Pythagorean Identity and Polar Curves; The Pythagorean Identity; Is My Answer Right?; Polar Graphs; A Gallery of Polar Curves;
Sum and Difference Identities; Angle Sum Identities; What's the Difference?; Guitar Harmonics; In Tune;
Double and Halfangle Formulas; Projectile Motion; Malus' Law; Planetary Motion; Circular Motion;
Law of Sines and Law of Cosines; The Montreal Tower; Can You Hear Me Now?; Play Ball!; Here Comes the Sun; Sines or Cosines?;
Secant and Tangent Functions; The Tangent Function; Graphing the Tangent Function; The Inverse Tangent Function; The Secant Function; Identities Involving Secant and Tangent;
Cosecant and Cotangent Functions; The Cotangent Function; Inverting the Cotangent Function; The Cosecant Function; Inverses of Secant and Cosecant;
Applications of Periodic Functions; Rising Carbon Dioxide; Car Wheels; Train Wheels; Amplitude Modulation
MARKET For anyone interested in improving trigonometric skills in preparation for Calculus courses. .
About the Author:
MyMathLab for Reasoning with Functions II was developed by the Charles A. Dana Center at The University of Texas-Austin. The Dana Center brings together experienced faculty from two- and four-year institutions to author, review, field-test, and revise the New Mathways Project curricular materials. The Dana Center develops and scales effective math and science innovations to support educators, administrators, and policy makers in creating seamless transitions throughout the K14 system for all students. Their work, based on research and two decades of experience, focuses on K-16 mathematics and science education with an emphasis on strategies for improving student engagement, motivation, persistence, and achievement. They develop innovative curricula, tools, protocols, and instructional supports and deliver powerful instructional and leadership development.
