Course Syllabus Overview

This syllabus outlines the main topics and suggested homework exercises for a college-level trigonometry course (Math 1316), based on the textbook by Lial, Hornsby, Schneider, and Daniels (Twelfth Edition). The course covers foundational and advanced concepts in trigonometry, including functions, identities, equations, applications, and vectors.

Course Topics and Structure

1. Angles and Triangles

• Angles: Definitions, measurement, and properties of angles.

• Angle Relationships and Similar Triangles: Understanding how angles relate within triangles and criteria for triangle similarity.

2. Trigonometric Functions

• Trigonometric Functions: Introduction to the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent).

• Using Definitions of Trigonometric Functions: Applying definitions to solve problems involving right triangles and the unit circle.

• Trigonometric Functions of Acute Angles: Calculating function values for acute angles.

• Trigonometric Functions of Non-acute Angles: Extending definitions to all angles using the unit circle.

• Approximations of Trigonometric Function Values: Using tables, calculators, or technology to estimate values.

3. Applications of Right Triangles

• Solutions and Applications of Right Triangles: Solving for unknown sides and angles using trigonometric ratios.

• Further Applications of Right Triangles: Real-world and advanced applications, including navigation and surveying.

4. Radian Measure and the Unit Circle

• Radian Measure: Definition and conversion between degrees and radians.

• Applications of Radian Measure: Arc length, area of sectors, and angular velocity.

• The Unit Circle and Circular Functions: Defining trigonometric functions for all real numbers using the unit circle.

• Linear and Angular Speed: Relationships between linear and angular velocity.

5. Graphs of Trigonometric Functions

• Graphs of the Sine and Cosine Functions: Amplitude, period, phase shift, and vertical shift.

• Translations of Graphs: Shifting and reflecting trigonometric graphs.

• Graphs of Tangent, Cotangent, Secant, and Cosecant: Key features and transformations.

6. Trigonometric Identities and Equations

• Fundamental Identities: Reciprocal, quotient, and Pythagorean identities.

• Verifying Trigonometric Identities: Techniques for proving identities.

• Sum and Difference Identities: Formulas for sine, cosine, and tangent of sums and differences of angles.

• Double-Angle and Half-Angle Identities: Special formulas for angles that are twice or half a given angle.

7. Inverse Trigonometric Functions and Equations

• Inverse Circular Functions: Definitions, domains, and ranges of inverse trigonometric functions.

• Trigonometric Equations: Solving equations involving trigonometric functions.

• Equations Involving Inverse Trigonometric Functions: Techniques for solving more complex equations.

8. Applications of Trigonometry and Vectors

• Oblique Triangles and the Law of Sines: Solving non-right triangles using the Law of Sines.

• The Ambiguous Case of the Law of Sines: Understanding when multiple solutions exist.

• The Law of Cosines: Solving triangles when two sides and the included angle or three sides are known.

• Vectors: Geometrically and algebraically defined vectors, applications, and the dot product.

Sample Table: Syllabus Structure and Homework Assignments

Key Formulas and Concepts

• Degree to Radian Conversion:

• Pythagorean Identity:

• Law of Sines:

• Law of Cosines:

• Double-Angle Formula for Sine:

• Sum Formula for Cosine:

Additional info:

• This syllabus provides a comprehensive roadmap for the study of trigonometry, including both theoretical foundations and practical applications.

• Homework assignments are designed to reinforce understanding and mastery of each topic.