MAC 1114: Trigonometry Syllabus and Course Overview

Course Overview: Trigonometry (MAC 1114)

Introduction

This course covers the fundamental concepts and applications of trigonometry, including trigonometric functions, their properties and graphs, inverse trigonometric functions, identities, equations, and applications to right and oblique triangles. Additional topics include vectors, polar coordinates, and complex numbers. The course is designed for students preparing for further study in mathematics, science, or engineering.

Course Objectives

• Understand and apply definitions of trigonometric functions using degrees and radians.

• Graph and analyze trigonometric and inverse trigonometric functions.

• Solve right and oblique triangles using trigonometric relationships and laws.

• Apply trigonometric identities and solve trigonometric equations.

• Work with vectors, polar coordinates, and complex numbers in trigonometric form.

Main Topics and Subtopics

1. Trigonometric Functions and Inverse Trigonometric Functions

• Definition of Trigonometric Functions: Based on angles measured in degrees and radians, relating sides and angles of right triangles.

• Unit Circle Approach: Defines sine, cosine, and tangent for all real numbers using the unit circle.

• Graphs: Graphs of sine, cosine, tangent, and their inverses, including amplitude, period, and phase shift.

• Inverse Functions: Definitions, domains, and ranges of arcsin, arccos, and arctan.

• Applications: Modeling periodic phenomena, such as sound and light waves.

• Example: Find the value of $\sin(30^\circ)$ and $\cos(\pi/3)$ using the unit circle.

2. Trigonometric Identities and Equations

• Fundamental Identities: Reciprocal, quotient, Pythagorean, double-angle, and half-angle identities.

• Solving Equations: Techniques for solving basic and advanced trigonometric equations.

• Example: Prove the identity $\sin^2\theta + \cos^2\theta = 1$.

3. Applications of Trigonometry

• Right Triangles: Use the Pythagorean Theorem and trigonometric ratios to solve for unknown sides and angles.

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

• Area of Triangles: Use the formula $A = \frac{1}{2}ab\sin C$ for non-right triangles.

• Example: Given two sides and the included angle, find the area of a triangle.

4. Polar Coordinates, Complex Numbers, and DeMoivre's Theorem

• Polar Coordinates: Represent points in the plane using $(r, \theta)$ instead of $(x, y)$.

• Graphing: Plot points and equations in polar coordinates.

• Complex Numbers: Express in polar form as $z = r(\cos\theta + i\sin\theta)$.

• DeMoivre's Theorem: For any integer $n$, $[r(\cos\theta + i\sin\theta)]^n = r^n[\cos(n\theta) + i\sin(n\theta)]$.

• Example: Find the cube roots of a complex number using DeMoivre's Theorem.

5. Vectors

• Definition: Quantities with both magnitude and direction, represented in component form.

• Operations: Addition, subtraction, and scalar multiplication of vectors.

• Applications: Solve problems involving forces, velocity, and other vector quantities.

• Example: Find the resultant of two vectors given in component form.

Key Formulas and Equations

• $\sin^2\theta + \cos^2\theta = 1$

• $\tan\theta = \frac{\sin\theta}{\cos\theta}$

• Law of Sines: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

• Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos C$

• Area of Triangle: $A = \frac{1}{2}ab\sin C$

• DeMoivre's Theorem: $[r(\cos\theta + i\sin\theta)]^n = r^n[\cos(n\theta) + i\sin(n\theta)]$

Course Structure and Grading

• Homework: 20% of grade, completed online via MyMathLab.

• Exams: 60% of grade, including in-class and optional final exam.

• Other Requirements: Scientific calculator, textbook access, and attendance as per college policy.

Sample Schedule (Excerpt)

Class	Date	Sections/Exam	Assignments Due
1	Tu 8/22	Orientation, 7.1
2	Th 8/24	7.2, 7.3
3	Tu 8/29	7.4, 7.5
4	Th 8/31	7.6, 7.7	7.1, 7.2 due at 11:59 pm
...	...	...	...

Additional Information

• Academic Success Center available for tutoring and support.

• Accommodations for students with disabilities are provided as per college policy.

• Textbook access is required; details provided in the syllabus.

• Adherence to college policies on attendance, academic honesty, and student conduct is mandatory.

Additional info: This summary is based on the course syllabus and includes expanded academic context for clarity and completeness.