Student Solutions Manual for Trigonometry

Mark Dugopolski was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an MS in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at Champaign—Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.

Table of Contents The table of contents below shows the review topics (bulleted text) that are integrated into the MyLab Math course. The Integrated Review includes worksheets, videos, and other materials designed to help students master these important topics.



Algebraic Prerequisites

P.1 The Cartesian Coordinate System
P.2 Functions
P.3 Families of Functions, Transformations, and Symmetry
P.4 Compositions and Inverses


Angles and the Trigonometric Functions

1.1 Angles and Degree Measure
1.2 Radian Measure, Arc Length, and Area
1.3 Angular and Linear Velocity
1.4 The Trigonometric Functions
1.5 Right Triangle Trigonometry
1.6 The Fundamental Identity and Reference Angles
Chapter 1 Integrated Review Topics:

Multiplying simple rational expressions
Using Rational Expressions in Conversions
Finding area and circumference of a circle using the standard formula.
Simplifying square roots.
Performing operations with square roots.
Using the Pythagorean theorem to find missing sides of a right triangle.
Finding center and radius of a circle given the equation for the circle.
Finding the inverse of a function.




Graphs of the Trigonometric Functions

2.1 The Unit Circle and Graphing
2.2 The General Sine Wave
2.3 Graphs of the Secant and Cosecant Functions
2.4 Graphs of the Tangent and Cotangent Functions
2.5 Combining Functions
Chapter 2 Integrated Review Topics:

Shifting graphs of algebraic functions horizontally and vertically.
Finding domain and range of algebraic functions; Reflecting, stretching, and shrinking of algebraic functions.
Writing equations of horizontal and vertical lines.
Performing arithmetic with fractions involving pi.
Finding horizontal and vertical asymptotes for rational functions.
Identifying domain and range of rational functions.




Trigonometric Identities

3.1 Basic Identities
3.2 Verifying Identities
3.3 Sum and Difference Identities for Cosine
3.4 Sum and Difference Identities for Sine and Tangent
3.5 Double-Angle and Half-Angle Identities
3.6 Product and Sum Identities
Chapter 3 Integrated Review Topics:

Recognizing identities in algebra.
Using the Fundamental Identity from Trigonometry to simplify expressions.
Using reciprocal identities to simplify expressions.
Multiplying binomials.
Squaring a binomial.
Factoring expressions into a product of two binomials.
Finding compositions of algebraic functions.
Proving that an equation is not an identity.
Operations with rational expressions in algebra.




Solving Conditional Trigonometric Equations

4.1 The Inverse Trigonometric Functions
4.2 Basic Sine, Cosine, and Tangent Equations
4.3 Equations Involving Compositions
4.4 Trigonometric Equations of Quadratic Type
Chapter 4 Integrated Review Topics:

Evaluating a composition of algebraic functions.
Identifying identities in trigonometry.
Solving proportions for a variable.
Solving for a variable in an algebraic equation.
Solving quadratic equations by factoring.
Solve quadratic equations by using the square root property.
Solve quadratic equations by using the quadratic formula.
Squaring each side of an equation and getting extraneous roots.
Domain and range of the trig functions.
Finding the exact values of the sine function.
Finding the exact values of secant, cosecant, and cotangent.




Applications of Trigonometry

5.1 The Law of Sines
5.2 The Law of Cosines
5.3 Area of a Triangle
5.4 Vectors
5.5 Applications of Vectors
Chapter 5 Integrated Review Topics:

Solving proportions for x.
Solving proportions using the inverse sine function.
Finding the area of a triangle using the standard formula.
Solving right triangles.
Finding the distance between two points with the distance formula.




Complex Numbers, Polar Coordinates, and Parametric Equations

6.1 Complex Numbers
6.2 Trigonometric Form of Complex Numbers
6.3 Powers of Roots of Complex Numbers
6.4 Polar Equations
6.5 Parametric Equations
New - 6.6 Fun with Polar and Parametric Equations
Chapter 6 Integrated Review Topics:

Simplifying square roots.
Adding and subtracting binomials.
Multiplying binomials.
Finding nth roots with 1/n notation.
Solving cubic equations.
Finding sine and cosine of large angles.