Math 041

Trigonometry and Analytic Geometry

4 credits

Blue Book Description: Straight lines; circles; functions and graphs; graphs of polynomial and rational functions; exponential and logarithmic functions; trigonometry; conic sections.

Pre-requisites: MATH 021 or satisfactory performance on the mathematics placement examination.

Pre-requisite for: MATH 140

Suggested Textbook:
Carl Stitz & Jeff Zeager: Precalculus, 3rd (corrected) Edition. This is a FREE open source textbook endorsed by the American Institute of Mathematics as part of their Open Textbook Initiative. Download at http://www.stitzzeager.com/szprecalculus07042013.pdf. If desired, printed copies of the book (in two paperback volumes) may be purchased on Lulu.com.
Check with your instructor to make sure this is the textbook used for your section.

Topics:
1 Relations and Functions
1.1 Sets of Real Numbers and the Cartesian Coordinate Plane
1.2 Relations
1.3 Introduction to Functions
1.4 Function Notation
1.5 Function Arithmetic
1.6 Graphs of Functions
1.7 Transformations

2 Linear and Quadratic Functions
2.1 Linear Functions
2.2 Absolute Value Functions
2.3 Quadratic Functions
2.4 Inequalities with Absolute Value and Quadratic Functions

3 Polynomial Functions
3.1 Graphs of Polynomials
3.2 The Factor Theorem and the Remainder Theorem
3.3 Real Zeros of Polynomials

4 Rational Functions
4.1 Introduction to Rational Functions
4.2 Graphs of Rational Functions
4.3 Rational Inequalities and Applications

5 Further Topics in Functions
5.1 Function Composition
5.2 Inverse Functions
5.3 Other Algebraic Functions

6 Exponential and Logarithmic Functions
6.1 Introduction to Exponential and Logarithmic Functions
6.2 Properties of Logarithms
6.3 Exponential Equations and Inequalities
6.4 Logarithmic Equations and Inequalities

7 Hooked on Conics
7.1 Introduction to Conics
7.2 Circles

10 Foundations of Trigonometry
10.1 Angles and their Measure
10.2 The Unit Circle: Cosine and Sine
10.3 The Six Circular Functions and Fundamental Identities
10.4 Trigonometric Identities
10.5 Graphs of the Trigonometric Functions
10.6 The Inverse Trigonometric Functions
10.7 Trigonometric Equations and Inequalities

11 Applications of Trigonometry (optional)
11.1 Applications of Sinusoids
11.2 The Law of Sines
11.3 The Law of Cosines