Course Overview

Introduction to Trigonometry (MATH 1316)

This course is designed for students preparing to take calculus, focusing on the fundamental concepts and applications of trigonometry. The curriculum covers trigonometric functions, their properties and graphs, inverse functions, trigonometric identities, equations, and applications involving triangles and logarithms. The course also emphasizes problem-solving skills and mathematical reasoning essential for further studies in mathematics and science.

Course Structure and Content

Main Topics and Chapters

• Chapter 6: Trigonometric Functions

  • 6.1 Angles & Their Measure

  • 6.2 Trigonometric Functions: Unit Circle

  • 6.3 Properties of Trigonometric Functions

  • 6.4 Sine & Cosine Graphs

  • 6.5 Tangent, Cotangent, Cosecant, Secant Graphs

  • 6.6 Phase Shift; Sine Curve Fitting

• Chapter 7: Analytic Trigonometry

  • 7.1 Inverse Sine, Cosine, & Tangent

  • 7.2 More Inverse Trigonometric Functions

  • 7.3 Trigonometric Equations

  • 7.4 Trigonometric Identities

  • 7.5 Sum & Difference Formulas

  • 7.6 Double-Angle & Half-Angle Formulas

  • 7.7 Product-to-Sum & Sum-to-Product Formulas

• Chapter 8: Applications of Trigonometric Functions

  • 8.1 Right Triangle Trigonometry; Applications

  • 8.2 The Law of Sines

  • 8.3 The Law of Cosines

  • 8.4 Area of a Triangle

  • 8.5 Simple Harmonic Motion

• Chapter 5: Exponential and Logarithmic Functions

  • 5.3 Exponential Functions

  • 5.4 Logarithmic Functions

  • 5.5 Properties of Logarithms

  • 5.6 Logarithmic and Exponential Equations

Student Learning Outcomes

Core Competencies

• Graphing and Properties: Recognize and use graphs and basic properties of elementary trigonometric functions and their inverses.

• Trigonometric Identities: Verify trigonometric identities and solve trigonometric equations using identities and properties.

• Geometric Problem Solving: Solve geometric problems involving triangles, including the use of the Law of Sines and Law of Cosines.

• Logarithmic Functions: Use properties of logarithms and solve equations involving logarithms.

• Personal Responsibility: Demonstrate accurate computation, logical reasoning, and completion of assessments.

Key Concepts and Definitions

Trigonometric Functions and Their Properties

• Angle Measurement: Angles can be measured in degrees or radians. One full revolution is or radians.

• Unit Circle: The unit circle is a circle of radius 1 centered at the origin. Trigonometric functions can be defined using the coordinates of points on the unit circle.

• Basic Trigonometric Functions: Sine, cosine, tangent, cosecant, secant, and cotangent are defined for all real numbers using the unit circle.

• Graphs: The graphs of sine and cosine are periodic with period , while tangent has period .

• Phase Shift: A horizontal shift in the graph of a trigonometric function, represented as .

Trigonometric Identities and Equations

• Pythagorean Identities:

• Sum and Difference Formulas:

• Double-Angle Formulas:

• Solving Equations: Use identities and algebraic manipulation to solve trigonometric equations for unknown angles.

Applications: Triangles and Harmonic Motion

• Law of Sines:

• Law of Cosines:

• Area of a Triangle:

• Simple Harmonic Motion: Described by equations such as , where is amplitude, is angular frequency, and is phase shift.

Exponential and Logarithmic Functions

• Exponential Function: , where and .

• Logarithmic Function: , the inverse of the exponential function.

• Properties of Logarithms:

• Solving Logarithmic and Exponential Equations: Use properties of logarithms and exponentials to isolate variables and solve equations.

Course Assessment and Grading

Assessment Components

• Homework: 15% of final grade; assigned for each section/topic.

• Attendance & Class Activities: 10% of final grade; participation and engagement required.

• Quizzes: 5% of final grade; regular weekly quizzes in MyLab.

• Tests: 45% of final grade; three in-person tests (each 15%).

• Final Exam: 25% of final grade; comprehensive and in-person.

Grading Scale

Marketable Skills Developed

• Apply trigonometric functions and identities to solve mathematical and real-world problems.

• Work confidently with degrees, radians, and circular measures for precise calculations.

• Simplify and solve equations using logarithmic functions effectively.

• Determine unknown sides and angles using trigonometric laws and techniques.

Course Schedule (Selected Weeks)

Academic Integrity and University Policies

• Strict adherence to academic honesty is required. Cheating, plagiarism, and other forms of academic misconduct are prohibited.

• Attendance is mandatory; excessive unexcused absences may result in being dropped from the course.

• Reasonable accommodations are available for students with disabilities through the Disability Resource Center.

• Support services are available for academic assistance, writing, mental health, and career planning.

Support Services

• Pathways Academic Assistance Center: Tutoring and academic support.

• Writing Center: Writing consultation for assignments.

• Success Peer Mentoring: Mentoring for academic and personal success.

• Jernigan Library: Access to books, technology, and research help.

• Mental Health & Well-Being: Counseling and crisis support.

• Disability Resources: Academic accommodations for students with disabilities.

• Advising: Academic and career advising.

• Career Engagement: Career planning and job search support.

• Student Government Association: Student representation and leadership opportunities.