MATH 122: Trigonometry and Precalculus – Syllabus and Study Guide

Course Overview

MATH 122: Trigonometry and Precalculus at Roosevelt University is designed to prepare students for the calculus sequence by deepening their understanding of trigonometry, functions, and systems of equations. The course covers foundational and advanced topics in precalculus, emphasizing conceptual understanding, problem-solving, and real-world applications.

Course Topics and Structure

Major Topics Covered

• Trigonometric Functions and Their Properties

• Basic Trigonometric Identities and Applications

• Inverse Functions (including exponential and logarithmic functions)

• Analytic Trigonometry

• Polar Coordinates and Polar Equations

• Complex Numbers and Vectors

• Systems of Equations, Matrices, and Determinants

These topics align with standard precalculus curriculum chapters, including functions and their graphs, trigonometric functions, analytic trigonometry, polar coordinates, vectors, and systems of equations.

Course Goals and Learning Objectives

• Write equations of circles in standard form using completing the square.

• Solve logarithmic and exponential problems; model data with exponential functions (growth and decay).

• Calculate angle measure, arc length, and area of a sector.

• Apply right triangle trigonometry to real-world problems.

• Find trigonometric functions of any angle and use the unit circle.

• Graph trigonometric functions and determine their domain, range, and period.

• Use and verify trigonometric identities, including sum/difference, double-angle, and half-angle formulas.

• Apply the Law of Sines and Law of Cosines to solve triangles.

• Work with polar coordinates, complex numbers, and vectors (including dot and cross products).

• Solve systems of linear equations using substitution, elimination, and matrices.

Weekly Schedule and Key Chapters

Week	Topics	Assessment
1	Angles and Their Measure (5.1), Right Triangle Trigonometry (5.2)	—
2	Values of Trigonometric Functions of Acute Angles (5.3)	HW #1
3	Trigonometric Functions of Any Angle (5.4), Unit Circle, Graphs of Sine and Cosine (5.5, 5.6)	HW #2, Quiz 1
4	Graphs of Tan, Cot, Sec, Csc (5.7), Phase Shift and Sinusoidal Curve Fitting (5.8)	HW #3, Quiz 2
5	Inverse Functions, Exponentials, Logarithms (4.2-4.3)	HW #3, Quiz 3
6	Review for Exam #1	HW #4, Exam #1
8	Inverse Sine, Cosine, Tangent (6.1), Inverse Trigonometric Functions (6.2)	HW #5, Quiz 4
9	Trigonometric Equations (6.3), Trigonometric Identities (6.4)	HW #6, Quiz 5
10	Sum/Difference, Double/Half-Angle, Product-to-Sum Formulas (6.5-6.7)	HW #7, Quiz 6
11	Applications Involving Right Triangles (7.1), Law of Sines (7.2), Law of Cosines (7.3)	HW #8, Quiz 7
12	Area of a Triangle (7.4), Vectors (8.4)	HW #10, Quiz 8
13	Dot Product (8.5), Vectors in 3D (8.6)	HW #11, Quiz 9
14	Vector Product (8.7), Systems of Linear Equations (10.1)	HW #12, Quiz 10
15	Review	HW #13
Finals	Comprehensive Final Exam	—

Key Mathematical Concepts

Trigonometric Functions

• Definition: Functions relating angles to ratios of sides in right triangles, extended to the unit circle.

• Basic Functions: Sine, Cosine, Tangent, Cotangent, Secant, Cosecant.

• Unit Circle: The unit circle approach allows for defining trigonometric functions for all real angles.

• Graphs: Each function has a characteristic graph, period, amplitude, and phase shift.

Trigonometric Identities and Equations

• Fundamental Identities: Pythagorean, reciprocal, quotient identities.

• Sum and Difference Formulas: Allow computation of trig values for sums/differences of angles.

• Double-Angle and Half-Angle Formulas: Useful for simplifying expressions and solving equations.

• Product-to-Sum and Sum-to-Product: Transform products of trig functions into sums or differences.

Inverse Trigonometric Functions

• Definition: Functions that reverse the effect of trigonometric functions, e.g., $y = \sin^{-1}(x)$.

• Domains and Ranges: Restricted to ensure each inverse is a function.

Exponential and Logarithmic Functions

• Exponential Functions: $f(x) = a^x$, where $a > 0$ and $a \neq 1$.

• Logarithmic Functions: $f(x) = \log_a(x)$, the inverse of the exponential function.

• Applications: Growth and decay models, solving equations involving exponents and logs.

Polar Coordinates and Complex Numbers

• Polar Coordinates: Represent points as $(r, \theta)$ instead of $(x, y)$.

• Complex Numbers: Numbers of the form $a + bi$, can be represented in polar form as $r(\cos \theta + i \sin \theta)$.

• De Moivre's Theorem: $(r(\cos \theta + i \sin \theta))^n = r^n (\cos n\theta + i \sin n\theta)$.

Vectors and Their Applications

• Definition: Quantities with both magnitude and direction.

• Operations: Addition, scalar multiplication, dot product, cross product (in 3D).

• Applications: Physics, engineering, navigation, and more.

Systems of Equations and Matrices

• Solving Methods: Substitution, elimination, and matrix methods (including inverses and determinants).

• Matrix Representation: Systems can be written as $A\vec{x} = \vec{b}$ and solved using $\vec{x} = A^{-1}\vec{b}$ if $A$ is invertible.

Assessment and Grading

Assignment	Percentage of Final Grade
Homework	20%
Online Quizzes	10%
Tests	40%
Final Exam	30%

Letter Grade Determination

Grade	Range (%)
A	93-100
A-	90-92.9
B+	87-89.9
B	83-86.9
B-	80-82.9
C+	77-79.9
C	73-76.9
C-	70-72.9
D+	67-69.9
D	63-66.9
D-	60-62.9
F	Below 60

Required Materials and Technology

• Textbook: Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry (Sullivan & Sullivan III, 5th Edition, Pearson)

• Graphing Calculator: Desmos, Geogebra, or TI-83/84 Plus

• Online Platform: MyLab Math with Pearson eText (access required)

Policies and Student Support

• Academic Integrity: Plagiarism and cheating are not tolerated. Limited, documented AI use is permitted for brainstorming and grammar-checking only.

• Disability Services: Accommodations available through the Learning Commons.

• Technology Support: Blackboard, MyLabMath, and campus IT resources are available.

• Student Resources: Tutoring, counseling, career services, food pantry, and more are accessible to all students.

Important Dates

• Course Start: January 21, 2025

• Last Day to Withdraw: March 20, 2026

• End of Classes: May 4, 2026

• Final Exam: May 6, 2026, 12:30–3:00 pm

Contact and Communication

• Instructor: Wilfredo Urbina-Romero

• Email: [e-mail]

• Office Hours: Mon & Wed 1:50–2:30 pm (in person or Zoom); Tues & Thurs 1:00–1:50 pm (Zoom)

Visual Reference

Additional info: This syllabus provides a comprehensive overview of the course structure, topics, and resources for a standard precalculus curriculum, supporting student preparation for calculus and related STEM fields.