MAC 1114 Trigonometry Syllabus Overview

Course Description

This course covers the fundamental concepts and applications of trigonometry, including trigonometric functions, their properties and graphs, inverse trigonometric functions, trigonometric identities, equations, solutions of triangles, polar coordinates, complex numbers, vectors, and related applications. It is designed for students preparing for advanced mathematics courses such as Calculus.

• Prerequisite: Completion of MAC 1105 or MAC 1106 with a grade of “C” or better, or appropriate placement test score.

• Required Materials: MyMathLab access, Sullivan Algebra and Trigonometry textbook (11th ed), reliable computer and internet access.

• Calculator Policy: Only non-graphing calculators without algebraic solvers are permitted (e.g., TI-30Xa, TI-30XIIs, Casio fx-260, Casio fx-300MS Plus).

Instructional Methods & Assessment

• Lecture Videos: Available for each section in MyMathLab.

• Homework: Administered through MyMathLab, due multiple times weekly, late submissions penalized.

• Quizzes: Given about once per unit, multiple attempts allowed, open book for later attempts.

• Proctored Exams: Four mandatory online proctored exams using Honorlock, timed and no notes allowed.

• Final Exam: Mandatory for all students.

Grading Policy

Course Intended Outcomes

1. Trigonometric Functions and Inverse Trigonometric Functions

This section focuses on understanding and applying the six basic trigonometric functions, their properties, and their graphs, as well as their inverses.

• Angle Measurement: Understand degree (decimal and DMS) and radian measures; convert between them.

• Applications: Solve problems involving arc length, sector area, and angular velocity.

• Trigonometric Functions: Define and understand sine, cosine, tangent, cotangent, secant, and cosecant using right triangle and unit circle approaches.

• Special Angles: Know function values for multiples of key angles using reference angles and triangles.

• Graphing: Graph trigonometric functions, identify period, amplitude, and phase shift.

• Inverse Functions: Define and graph inverse trigonometric functions, specify domain and range, and find their values.

• Modeling: Construct trigonometric models for periodic phenomena and solve related problems.

2. Trigonometric Identities and Conditional Equations

This section covers the fundamental identities and equations in trigonometry, including their application and proof.

• Identities: Know and apply reciprocal, quotient, Pythagorean, double angle, half-angle, sum and difference, product-to-sum, and sum-to-product identities.

• Proofs: Prove trigonometric identities.

• Equations: Solve trigonometric equations algebraically and graphically.

3. Solutions of Triangles

This section addresses solving both right and oblique triangles using trigonometric methods and formulas.

• Right Triangles: Solve using the Pythagorean Theorem and trigonometric functions.

• Oblique Triangles: Solve using the Law of Sines and Law of Cosines.

• Area: Find the area of any triangle using appropriate formulas.

• Applications: Solve real-world problems involving triangles.

4. Polar Coordinates, Trigonometric Form of Complex Numbers, and DeMoivre’s Theorem

This section explores polar coordinates, complex numbers in trigonometric form, and DeMoivre’s Theorem for powers and roots.

• Polar Coordinates: Plot points and convert between polar and rectangular forms.

• Polar Equations: Graph curves defined by polar equations.

• Complex Numbers: Plot in the complex plane, convert between rectangular and polar forms, multiply/divide in polar form.

• DeMoivre’s Theorem: Find powers and roots of complex numbers using .

5. Vectors

This section covers vector operations, descriptions, and applications in two and three dimensions.

• Vector Forms: Convert between rectangular and polar (magnitude, direction) descriptions.

• Resultant: Find the sum of vectors algebraically and geometrically.

• Dot Product: Calculate the dot product and find the angle between vectors.

• Components: Resolve vectors into horizontal and vertical components.

• Applications: Use vectors to model velocity and force problems.

• Three Dimensions: Perform vector operations including the cross product in three dimensions.

Additional Course Information

• Academic Integrity: All forms of academic dishonesty are prohibited; violations result in automatic zero for the assignment.

• Accommodations: Students requiring accommodations must contact the Office of Services to Students with Disabilities and arrange with the instructor within the first two weeks.

• Student Assistance: Free, confidential counseling available through HCC’s Student Assistance Program.