Course Overview

This syllabus outlines the structure, content, and expectations for MATH 2412: Precalculus at Tarrant County College. The course prepares students for calculus by covering advanced algebra, trigonometry, polar coordinates, vectors, complex numbers, and analytic geometry. The course emphasizes critical thinking, communication, and quantitative skills.

Course Description

• Combined study of algebra, trigonometry, and other topics for calculus readiness.

• Prerequisite: MATH-1314 or MATH-1316 with a minimum grade of C or appropriate placement test score.

• Co-requisite: MATH 2412L.

Course Goals and Learning Outcomes

Upon successful completion, students will be able to:

• Understand properties of functions: including trigonometric functions, their domains and ranges, inverse functions, and notation.

• Solve algebraic and transcendental equations: including trigonometric equations and identities.

• Apply graphing techniques: to trigonometric and inverse trigonometric functions.

• Compute trigonometric values: for key angles using both degree and radian measures, unit circle, and right triangle approaches.

• Prove trigonometric identities: using fundamental identities (ratio, reciprocal, Pythagorean, cofunction).

• Solve triangles: using right triangle methods, Law of Sines, and Law of Cosines.

• Apply trigonometry to real-world problems: including arc length, area of sectors, angular and linear velocity.

• Examine complex numbers: operations, conversions, powers, and roots.

• Explore analytic geometry: vectors, parametric equations, conic sections, polar coordinates.

• Understand sequences and series: arithmetic, geometric, summation notation, binomial theorem.

Major Topics and Subtopics

Trigonometric Functions and Their Properties

Trigonometric functions are fundamental in precalculus, describing relationships between angles and sides in triangles and periodic phenomena.

• Definition: Functions such as sine, cosine, tangent, cotangent, secant, and cosecant relate angles to ratios of sides in right triangles and points on the unit circle.

• Domain and Range: For example, and have domains and ranges .

• Inverse Functions: Inverse trigonometric functions (arcsin, arccos, arctan) allow solving for angles given ratios.

• Notation: , , .

• Example: ; .

Solving Trigonometric Equations and Identities

Solving equations and verifying identities is essential for understanding trigonometric relationships.

• Single Function Equations: Solve for .

• Using Identities: Apply identities such as .

• Multiple Angles: Solve equations like .

• Example: .

Graphing Trigonometric and Inverse Functions

Graphing helps visualize periodicity, amplitude, and phase shifts.

• Basic Graphs: , , .

• Amplitude: Maximum value from the midline; for , amplitude is .

• Period: Length of one cycle; for , period is .

• Phase Shift: Horizontal shift; for , phase shift is .

• Inverse Graphs: , , .

• Example: Graph .

Unit Circle and Angle Measurement

The unit circle is a central tool for defining trigonometric functions and converting between degrees and radians.

• Degree and Radian Measure: radians.

• Unit Circle Definition: For angle , and are the and coordinates of the point on the unit circle.

• Right Triangle Approach: Trigonometric ratios based on triangle sides.

• Exact Values: , .

• Example: Find .

Trigonometric Identities

Identities are equations true for all values in the domain and are used to simplify expressions and solve equations.

• Ratio Identities: .

• Reciprocal Identities: , .

• Pythagorean Identities: .

• Cofunction Identities: .

• Example: Verify .

Solving Triangles: Right and Oblique

Solving triangles involves finding unknown sides or angles using trigonometric relationships.

• Right Triangle Problems: Use basic trigonometric ratios.

• Law of Sines: .

• Law of Cosines: .

• Choosing Techniques: Use Law of Sines for ASA, AAS, or Law of Cosines for SAS, SSS.

• Example: Solve triangle with , , .

Applications of Trigonometry

Trigonometry is used in real-world applications such as measuring distances, velocities, and areas.

• Arc Length: (with in radians).

• Area of Circular Sector: .

• Angular Velocity: .

• Linear Velocity: .

• Applied Right Triangle Problems: Height and distance calculations.

• Example: Find the area of a sector with , .

Complex Numbers

Complex numbers extend the real numbers and are used in advanced algebra and trigonometry.

• Operations: Addition, subtraction, multiplication, division.

• Rectangular Form: .

• Trigonometric Form: .

• Multiplication/Division in Trigonometric Form: .

• De Moivre’s Theorem: .

• Example: Find for .

Analytic Geometry: Vectors, Parametric Equations, Conic Sections, Polar Coordinates

Analytic geometry explores geometric objects using algebraic equations.

• Vectors: Represented as ; vector arithmetic includes addition, subtraction, scalar multiplication.

• Parametric Equations: Express curves as , .

• Conic Sections: Parabola, ellipse, hyperbola; standard equations:

  • Parabola:

  • Ellipse:

  • Hyperbola:

• Polar Coordinates: ; conversion between polar and rectangular: , .

• Polar Equations: .

• Example: Convert to rectangular form.

Sequences, Series, and Binomial Theorem

Sequences and series are foundational for calculus and discrete mathematics.

• Sequence: Ordered list of numbers; arithmetic sequence: .

• Series: Sum of sequence terms; geometric series: .

• Summation Notation: .

• Binomial Theorem: .

• Example: Find the sum of the first 5 terms of .

Course Outline and Schedule

Grading Policy

Grade Scale:

Important Dates

• Classes Begin: February 4, 2026

• Spring Break: March 16-22, 2026

• Course Drop Deadline: April 30, 2026

• Final Exam Week: May 7-13, 2026

Attendance and Classroom Policies

• Regular attendance and participation are required.

• Homework must be submitted on time; no late assignments accepted.

• Academic honesty is strictly enforced.

• Electronic devices are prohibited during tests except authorized calculators.

Additional Information

• Support hours and instructor contact provided for student assistance.

• Academic Continuity Plan ensures course completion in case of emergencies.

• Title IX policies protect student safety and privacy.

Additional info: This syllabus covers all major precalculus topics relevant to college-level study, including trigonometric functions, identities, equations, applications, complex numbers, vectors, polar coordinates, conic sections, sequences, and series. The course is structured to prepare students for calculus and advanced mathematics.