Table of Contents | Areas of Study | Mathematics | MATH114 syllabus

COURSE NUMBER:		MATH114
COURSE TITLE:		Trigonometry
IAI CODE(S):		MTM 901
SEMESTER CREDIT HOURS:		3

COURSE DESCRIPTION:
The study of the six trigonometric and circular functions, their inverses, the identities associated with these functions, and their application to problem solving. A graphing calculator is recommended.

PREREQUISITES:
Appropriate score on Math Placement Test, grade of "C" or better in Math 111 or Math 112, or consent of instructor.

COURSE OBJECTIVES / GOALS:
The student should be able to:

• Define and use both degree and radian measure.
• Define the six trigonometric functions using a point on the terminal side of an angle in standard position.
• Define the six trigonometric functions of both acute and non-acute angles.
• Define the six circular functions.
• Graph the six circular functions and translations of these functions.
• Define the inverses of the six trigonometric functions and use to solve trigonometric equations.
• Solve triangles using trigonometric identities and algebraic procedures.
• Use fundamental trigonometric identities in verifying identities and solving equations.
• Use methods of trigonometry to solve application problems.
• Use graphing utilities on a calculator and a computer.

TOPICAL OUTLINE:

• Geometric angle and triangle relationships.
• The six trigonometric functions of an angle in standard position with respect to a point on the terminal side of an angle.


• Defining functions
• Evaluating functions and determining signs of each function
• Finding values of quadrantal angles


  
• Fundamental identities.


• Reciprocal identities
• Quotient identities
• Pythagorean identities
• Negative angle identities
• Confunction identities


  
• The six trigonometric functions of acute angles in a right triangle.


• Defining functions in terms of an angle in a right triangle
• Determining exact values of special acute angles and quadrantal angles
• Determining reference angles and evaluating trigonometric functions for non-acute angles


  
• Solving right triangles and applying to real world situations.
• Using calculator to find approximations.
• Radian measure and conversions between degrees and radians.
• The six circular functions.


• Defining the trigonometric functions in terms of real numbers
• Evaluating circular functions
• Applying radian measure:  arc length, area of a sector of a sector, linear velocity, and angular velocity


  
• Graphs of the six circular functions.


• Basic graphs of each function
• Domain, range and period of each function
• Techniques of graphing using translations and amplitude, vertical translations, phase shifts, and period
• Using the graphing utility Mathematica to graph the circular functions


  
• Verifying identities.


• Techniques for verifying identities
• Sum and difference identities
• Double and half angle identities
• Using special identities in problem solving


  
• Inverse trigonometric functions


• Defining inverse functions, their domains and ranges
• Using inverse trigonometric functions to solve trigonometric equations


  
• Solving oblique triangles


• Law of sines
• Law of cosines


  
• Finding area of any triangle
• Complex numbers (optional)


• Operations with complex numbers
• Trigonometric form of a complex numbers
• Powers and quotients for a complex number and DeMoivre's Theorem

TEXTBOOK / SPECIAL MATERIALS:

• Trigonometry, Fourth Edition, by McKeaque, Saunders College Publishing, 1999.

EVALUATION:

• Quizzes and homework
• Five or six 50 minute exams
• Comprehensive final exam
• Determination of grade is according to the following scale:


• A = 90% - 100%
• B = 80% -   89%
• C = 70% -   79%
• D = 60% -   69%


  
• A grade of C is highly recommended before entering trig based Calculus or Physics.

REVISION:
Fall 2001 10/01/2001

RECORD UPDATED:
2002/04/02 07:18:58