Course Overview

Introduction to Trigonometry with Analytic Geometry

This course, MATH 137: Trigonometry with Analytic Geometry, provides an in-depth study of trigonometric concepts, vectors, analytic geometry, and their applications. The course is designed for students who have completed Intermediate Algebra and are preparing for further studies in mathematics, science, or engineering.

• Prerequisite: Intermediate Algebra (Math 043) or appropriate placement.

• Textbook: Algebra & Trigonometry by Sullivan, 12th Edition (Pearson).

• Calculator: Scientific calculator (e.g., TI-30XS Multiview); graphing calculators and CAS devices are not permitted on exams.

• Course Format: Online, with modules, homework, quizzes, and proctored exams.

Major Course Learning Objectives

Core Competencies and Skills

Upon successful completion, students will be able to:

1. Convert between degrees and radians.

2. Find trigonometric function values for any angle (degree or radian measure).

3. Solve right triangles.

4. Solve oblique triangles using the Law of Sines and Law of Cosines.

5. Use and apply properties of vectors.

6. Graph trigonometric functions.

7. Use trigonometric identities to verify equivalencies.

8. Solve trigonometric equations.

9. Convert between rectangular and polar coordinate systems.

10. Apply properties of complex numbers in rectangular and polar forms.

11. Determine features of conic sections from standard equations.

12. Graph circles, parabolas, ellipses, and hyperbolas.

13. Apply these principles to solve practical applications.

14. Use technology appropriately to enhance learning.

Course Content Areas

Topics Covered

• Complex Numbers

• Angles and Trigonometric Functions

• Right and Oblique Triangles

• Vectors

• Graphs of Trigonometric Functions

• Trigonometric Equations and Identities

• Rectangular and Polar Coordinates

• Rational Functions

• Conic Sections

Module and Assignment Structure

Organization of Learning Activities

• Each module includes homework, quizzes, and check-in assignments.

• Homework is completed in MyLab Math with multiple attempts and help features.

• Quizzes are timed, with limited attempts and no help features.

• Exam review and prep assignments are provided before the midterm and final exams.

• Proctored midterm and final exams are required, with formula sheets and a blank unit circle provided.

Key Mathematical Topics (as indicated by syllabus and assignment schedule)

Trigonometric Functions and Angles

Trigonometric functions relate angles to ratios of sides in right triangles and to coordinates on the unit circle.

• Degree and Radian Measure: Conversion between degrees and radians is essential for solving trigonometric problems.

• Unit Circle: The unit circle is a fundamental tool for understanding trigonometric functions and their values at key angles.

• Trigonometric Functions: Sine, cosine, tangent, cosecant, secant, and cotangent.

Formula for Degree-Radian Conversion:

Solving Triangles

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

• Right Triangles: Use of basic trigonometric ratios and the Pythagorean Theorem.

• Oblique Triangles: Application of the Law of Sines and Law of Cosines.

Law of Sines:

Law of Cosines:

Graphs of Trigonometric Functions

Graphing trigonometric functions helps visualize their periodic nature and transformations.

• Amplitude, Period, Phase Shift, and Vertical Shift: Key parameters in function transformations.

• Standard Sine and Cosine Graphs: and

Period Formula:

Trigonometric Identities and Equations

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

• Pythagorean Identities:

• Angle Sum and Difference Identities:

• Double-Angle and Half-Angle Identities

Vectors

Vectors are quantities with both magnitude and direction, used in physics and engineering applications.

• Vector Representation: In component form as

• Magnitude:

• Direction: Angle with respect to the positive x-axis.

Complex Numbers

Complex numbers extend the real numbers and can be represented in rectangular or polar form.

• Rectangular Form:

• Polar Form: or

• Conversion: ,

Rectangular and Polar Coordinates

Coordinate systems are used to describe the location of points in the plane.

• Rectangular (Cartesian) Coordinates:

• Polar Coordinates: , where is the distance from the origin and is the angle from the positive x-axis.

• Conversion: ,

Conic Sections

Conic sections are curves obtained by intersecting a plane with a double-napped cone: circles, parabolas, ellipses, and hyperbolas.

• Standard Equations:

  • Circle:

  • Parabola: or

  • Ellipse:

  • Hyperbola:

Grading and Assessment Structure

Assignment Types and Weighting

Grading Scale:

Academic Integrity and Course Policies

Expectations and Procedures

• All work must be your own; use of AI or unauthorized resources is prohibited.

• Late homework and quizzes incur a 2% per day penalty.

• Proctored exams require a valid photo ID and submission of scratch work.

• No extra credit is offered; grading is standardized and transparent.

• Communication with the instructor is encouraged for any issues or exceptional circumstances.

Course Schedule and Module Topics (Sample)

Module Breakdown (Based on Assignment Titles)

• Module 1: Trigonometric Functions (Sections 7.1–7.5)

• Module 2: Advanced Trigonometric Functions and Identities (Sections 7.6–8.2)

• Module 3: Trigonometric Equations and Applications (Sections 8.3–8.7)

• Module 4: Midterm Exam Preparation and Assessment

• Module 5: Applications of Trigonometry and Introduction to Polar Coordinates (Sections 9.1–10.1)

• Module 6: Polar Coordinates, Vectors, and Further Applications (Sections 10.2–10.5)

• Module 7: Analytic Geometry and Conic Sections (Sections 11.2–11.4, 2.4)

• Module 8: Final Exam Preparation and Assessment

Additional info: The module and section numbers correspond to the Sullivan textbook and align with standard precalculus topics, including trigonometric functions, identities, equations, vectors, polar coordinates, and conic sections.

Conclusion

This syllabus outlines a comprehensive precalculus course focusing on trigonometry and analytic geometry. Mastery of these topics will prepare students for calculus and related fields. Students are encouraged to engage actively with the material, utilize available resources, and maintain academic integrity throughout the course.