Precalculus Trigonometry: Course Structure, Topics, and Key Concepts (MATH 110 Syllabus Study Guide)

Course Overview

Introduction to Trigonometry in Precalculus

This course syllabus outlines the structure and content for MATH 110: University Mathematics B II – Trigonometry, a college-level precalculus course. The course covers fundamental trigonometric concepts, functions, identities, equations, and their applications, preparing students for further study in mathematics and related fields.

• Prerequisites: Completion of MATH 108 or placement by examination.

• Credits: 4

• Textbook: Precalculus by Ratti and McWaters, 5th Edition (Pearson)

Course Policies and Structure

Grading and Assessment

Student performance is evaluated through homework, quizzes, midterm exams, and a final exam. The grading breakdown is as follows:

Component	Weight
Homework and Quizzes	25%
Common Midterm Exam I	15%
Common Midterm Exam II	15%
Final Exam	30%

Letter grades are assigned based on a standard scale (A: 90-100, B+: 83-87, etc.). Attendance is mandatory.

Homework and Exam Policies

• Homework: Regular assignments, including hand-written and online problems, are required.

• Exams: Three common midterms and one comprehensive final exam are scheduled throughout the semester.

• Quizzes: Weekly quizzes assess understanding of current topics.

• Makeup Policy: No makeup quizzes or exams except for documented emergencies.

Course Outline and Main Topics

Overview of Topics

The syllabus provides a detailed week-by-week outline of topics, homework, and practice problems. The main topics are grouped as follows:

1. Trigonometric Functions and Identities

• Angles and Their Measures: Understanding degrees, radians, and conversions between them.

• Trigonometric Functions: Definitions of sine, cosine, tangent, and their reciprocals.

• Right Triangle Trigonometry: Application of trigonometric ratios to solve triangles.

• Trigonometric Identities: Fundamental identities such as Pythagorean, reciprocal, quotient, and cofunction identities.

• Sum and Difference Formulas: Formulas for $an(A \\pm B)$, $ext{sin}(A \\pm B)$, $ext{cos}(A \\pm B)$.

• Double and Half Angle Formulas: Expressions for $ext{sin}(2A)$, $ext{cos}(2A)$, $ext{tan}(2A)$, and their half-angle counterparts.

Example: The sine of a sum: $\sin(A+B) = \sin A \cos B + \cos A \sin B$

2. Graphs of Trigonometric Functions

• Basic Graphs: Plotting sine, cosine, and tangent functions, identifying period, amplitude, and phase shift.

• Transformations: Effects of changes in amplitude, period, and phase on the graphs.

• Inverse Trigonometric Functions: Definitions and graphs of $\arcsin(x)$, $\arccos(x)$, $\arctan(x)$.

Example: The graph of $y = \sin(x)$ has amplitude 1 and period $2\pi$.

3. Trigonometric Equations and Applications

• Solving Trigonometric Equations: Techniques for finding all solutions within a given interval.

• Applications: Real-world problems involving angles of elevation/depression, harmonic motion, and periodic phenomena.

• Law of Sines and Law of Cosines: Solving oblique triangles.

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

4. Analytic Trigonometry

• Product-to-Sum and Sum-to-Product Formulas: Converting products of sines and cosines to sums or differences.

• Trigonometric Formulas for Multiple Angles: Using identities to simplify expressions.

Example: Product-to-sum: $\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]$

5. Applications of Trigonometry

• Polar Coordinates: Representing points in the plane using radius and angle.

• Graphs of Polar Equations: Plotting curves such as circles and ellipses in polar form.

• Areas of Polygons Using Trigonometry: Calculating area using trigonometric relationships.

Example: Area of a triangle: $A = \frac{1}{2}ab\sin C$

6. Exponential and Logarithmic Functions

• Exponential Functions: Functions of the form $f(x) = a^x$.

• Logarithmic Functions: Inverse of exponential functions, $f(x) = \log_a x$.

• Properties and Rules: Laws of exponents and logarithms, including change of base formula.

Example: Change of base: $\log_b a = \frac{\log_c a}{\log_c b}$

7. Limits (Introduction)

• Numerical and Graphical Approaches: Estimating limits from tables and graphs.

• Properties of Limits: Basic limit laws and their applications.

Example: $\lim_{x \to a} f(x)$

Course Schedule and Important Dates

Date	Event
September 1, 2025	Labor Day
September 2, 2025	First Day of Classes
October 2, 2025	Common Exam I
October 29, 2025	Common Exam II
December 3, 2025	Common Exam III
December 14-20, 2025	Final Exam Week

Additional Resources

• Math Tutoring Center: Located in the Central King Building, Lower Level, Room G11.

• Accessibility Services: Contact the Office of Accessibility Resources and Services for accommodations.

Summary Table: Main Trigonometric Topics

Topic	Key Concepts	Example Formula
Angles and Measures	Degrees, radians, conversions	$\theta_{\text{radians}} = \frac{\pi}{180} \theta_{\text{degrees}}$
Trigonometric Functions	Sine, cosine, tangent, reciprocals	$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
Identities	Pythagorean, sum/difference, double angle	$\sin^2 \theta + \cos^2 \theta = 1$
Graphs	Period, amplitude, phase shift	$y = A \sin(Bx + C) + D$
Equations	Solving for angles, applications	$\sin x = k$
Law of Sines/Cosines	Oblique triangles	$\frac{a}{\sin A} = \frac{b}{\sin B}$
Polar Coordinates	Radius and angle representation	$(r, \theta)$

Additional info: The syllabus also includes policies on academic integrity, attendance, and accessibility, as well as a detailed schedule of lectures, homework, and exams. The course is designed to provide a comprehensive foundation in trigonometry for students pursuing STEM degrees.