College Algebra & Trigonometry for Engineers and Scientists II: Course Syllabus Study Guide

Course Overview

Course Description

This course, College Algebra & Trigonometry for Engineers and Scientists II (MATH 104), is a continuation of Math 103 and is designed for students in engineering and science disciplines. The curriculum covers advanced topics in algebra and trigonometry, including exponential, logarithmic, and trigonometric functions, their graphs, the geometry of triangles, trigonometric identities, and the binomial theorem. The course emphasizes mathematical reasoning, problem-solving, and quantitative analysis.

Student Learning Objectives

Core Competencies

• Polynomial Functions: Find zeroes, graph functions, and analyze their properties.

• Exponential and Logarithmic Functions: Solve equations, understand definitions, domains, ranges, and graph these functions.

• Trigonometric Functions: Define trigonometric functions using right triangles for any angle, apply the law of sines and cosines, and evaluate function values for special angles.

• Systems of Equations: Solve linear and nonlinear systems using elimination and substitution methods.

• Trigonometric Identities: Apply co-function, sum/difference, double angle, and half-angle formulas.

• Binomial Theorem: Understand and apply the binomial theorem in algebraic contexts.

Key Topics and Concepts

Polynomial Functions

Polynomial functions are algebraic expressions involving powers of variables. Students will learn to:

• Find zeroes of polynomial functions.

• Graph polynomial functions using point selection, transformations, and the leading coefficient test.

• Analyze the behavior of polynomials at infinity and near their zeroes.

• Example: For $f(x) = x^3 - 4x^2 + x + 6$, find the zeroes by factoring or using the Rational Root Theorem.

Exponential and Logarithmic Functions

These functions model growth and decay processes and are fundamental in science and engineering.

• Definitions: $f(x) = a^x$ (exponential), $f(x) = \log_a(x)$ (logarithmic).

• Domains and ranges: Exponential functions are defined for all real numbers; logarithmic functions are defined for positive real numbers.

• Solving equations: Use properties of exponents and logarithms to solve equations such as $a^x = b$ or $\log_a(x) = y$.

• Example: Solve $2^x = 8$ by recognizing $8 = 2^3$, so $x = 3$.

Trigonometric Functions and Triangle Geometry

Trigonometric functions relate angles to side lengths in right triangles and are used to solve problems involving triangles.

• Definitions: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

• Law of Sines: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$.

• Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos C$.

• Special angles: Values for $0^, 30^, 45^, 60^, 90^$.

• Example: In a triangle with sides $a = 5$, $b = 7$, and angle $C = 60^$, use the Law of Cosines to find $c$.

Trigonometric Identities

Identities are equations involving trigonometric functions that hold for all values of the variables.

• Co-function identities: $\sin(90^ - x) = \cos(x)$.

• Sum and difference formulas: $\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B$.

• Double angle formulas: $\sin(2x) = 2\sin x \cos x$.

• Half-angle formulas: $\sin^2(x) = \frac{1 - \cos(2x)}{2}$.

• Example: Prove $\sin(2x) = 2\sin x \cos x$ using sum formulas.

Systems of Equations

Systems of equations involve solving for multiple variables using multiple equations.

• Elimination method: Add or subtract equations to eliminate a variable.

• Substitution method: Solve one equation for a variable and substitute into another.

• Nonlinear systems: May involve quadratic or other nonlinear equations.

• Example: Solve $x + y = 5$ and $x - y = 1$ by elimination.

Binomial Theorem

The binomial theorem provides a formula for expanding expressions of the form $(a + b)^n$.

• Formula: $(a + b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$.

• Applications: Used in algebraic expansions and probability.

• Example: Expand $(x + 2)^3$ using the binomial theorem.

Course Policies and Grading

Grading Scale

Letter Grade	Numerical Range
A	92 - 100
A-	90 - 91
B+	88 - 89
B	82 - 87
B-	80 - 81
C+	78 - 79
C	70 - 77
C-	68 - 69
D+	66 - 67
D	60 - 65
F	0 - 59

Grading Allocation

Graded Component	Weight (%)
Homework Assignments	25
Participation Assignments	20
Tests	45
Final Exam	10
Total	100

Course Requirements and Policies

• Prerequisites: Completion of MATH 103 with a grade of "C" or better.

• Textbook: Algebra & Trigonometry (ISBN: 978013590967).

• Learning Management System: Canvas is used for assignments, grades, and communication.

• Attendance and Participation: Regular attendance and active participation are required.

• Make-Up Exams: Allowed only with official written excuses.

• Late Work: No late assignments accepted except for homework with a penalty.

• Extra Credit: Not available.

• AI Policy: Use of generative AI (e.g., ChatGPT) is not permitted for assignments.

Support and Resources

• Tutorial Services: Free tutoring available through Upswing and the Center for Academic Excellence.

• Technical Support: Client Technology Services provides IT support.

• Accessibility: Accommodations available through the Office of Accessibility Resources.

• Counseling Services: Confidential counseling for students in need.

• Veteran & Military Affairs: Support for veteran and military students.

University Policies

• Academic Integrity: Cheating, plagiarism, and other forms of dishonesty are strictly prohibited.

• Title IX: Policies and resources for sexual misconduct and relationship violence.

• FERPA: Protection of student educational records.

• Grade Appeal: Procedures for appealing grades.

• Student Conduct: Rules and regulations for student behavior.

Useful Links

• Aggies Care

• Student Computer Recommendations

• Office of Accessibility Resources

• Title IX

• Client Technology Services

• Division of Student Affairs

• Student Handbook

• Graduate Catalog

• Student Activity Travel Waiver

• Title IX Policies

• FERPA

• Student Complaint Procedure

• Undergraduate Bulletins

Additional info: The course syllabus aligns closely with the Precalculus topics listed, including polynomial, exponential, logarithmic, and trigonometric functions, systems of equations, and the binomial theorem. The study guide above is structured to provide a comprehensive overview for exam preparation and course understanding.