MATH 1316

MATH 1316

INSTRUCTOR:  Fred Warnke
DEPARTMENT:  Mathematics
PHONE:  956-882-6609
COURSE NO:  Math 1316
COURSE TITLE:  Trigonometry

COURSE DESCRIPTION:  Topics include trigonometric functions, right triangles, radian measure and circular functions, graphs of trigonometric functions, identities, inverse trigonometric functions, trigonometric equations, oblique triangles, complex numbers, and the practical problems.  Lec 3, Cr 3, Prerequisite: Math 1314 with a minimum grade of "C" or equivalent as determined by the mathematics assessment test.


           Text:  Trigonometry, 7th Edition, by Lial, Hornsby, and Schneider
           A TI graphing calculator or equivalent is highly recommended for this course
           A bluebook is required for each test


  I.  The Trigonometric Functions
                1.  Basic concepts
                2.  Angles
                3.  Angle relationships and similar triangles
                4.  Definitions of the trigonometric functions
                5.  Using the definitions of the trigonometric functions
 II.  Acute Angles and Right Triangles
                1.  Trigonometric function of acute angles
                2. Trigonometric function of non-acute angles
                3.  Finding trigonometric function values using a calculator
                4.  Solving right triangles
                5.  Further applications of right triangles
III. Radian Measure and the Circular Functions
                1.  Radian measure
                2.  Application of radian measure
                3.  Circular functions of real numbers
                4.  Linear and angular velocity
IV.  Graphs of the Circular Functions
                1.  Graphs of sine and cosine functions
                2.  Translating graphs of the sine and cosine functions
                3.  Graphs of the other circular functions
V.  Trigonometric Identities
                1.  Fundamental identities
                2.  Verifying trigonometric identities
                3.  Sum and difference identities for cosine
                4.  Sum and difference identities for sine and tangent
                5.  Double-angle identities
                6.  Half-angle identities
VI.  Inverse Trigonometric Functions and Trigonometric Equations
                1.  Inverse trigonometric functions
                2.  Trigonometric equations I
                3.  Trigonometric equations II
                4.  Equations Involving Inverse trigonometric functions
VII.  Applications of Trigonometry and Vectors
                 1.  Oblique triangles and the law of sines
                 2.  The ambiguous case of the law of sines
                 3.  The law of cosines

Reading:  Reading at the college level means the ability to analyze and interpret a variety of printed materials - books, articles, and documents.  In this course the student will be required to read the chapter sections to foster understanding of the mathematical concepts being discussed.  Listening to your instructor's lecture is not sufficient.  You must reinforce what you hear in class with what you read outside of class.  The textbook for this course gives the student many opportunities to read mathematics and to interpret theorems and definitions.

Writing:  Competency in writing is the ability to produce clear, correct, and coherent prose, adapted to purpose, occasion, and audience.  Writing ability can be acquired only through practice and reflection.  Some homework exercises will require you to read and write rather than compute a numerical answer.  Communicating mathematical ideas to others by writing is an important skill that needs to be developed.  Chapter tests will include questions which will require you to explain a given mathematical procedure or concept in writing.

Critical Thinking:  Critical thinking uses methods for applying both qualitative and quantitative skills analytically and creatively to subject matter in order to construct strategies in problem solving.  In this course, the student is expected to apply arithmetic, algebraic, higher order thinking, and statistical methods to modeling and solving real-world problems.  Problem-solving techniques are emphasized throughout this course.  The student will be expected to analyze problems and determine a means of solving the problems.

Computer Literacy:  Computer literacy means the ability to use computer-based technology in communicating, solving problems, and acquiring knowledge.  In this class the focus is on solving problems.  The student will be required to use appropriate technology to enhance mathematical thinking and understanding and to solve problems and judge the reasonableness of the results.  A computer project will require that you use a spreadsheet to solve given problem.

COURSE OBJECTIVES:  The student will be familiar with

  1.  basic terminology, degree measure, angle in standard position and coterminal angles.
  2.  geometric properties of angles and triangles
  3.  trigonometric functions and quadrantal angles.
  4.  reciprocal identities, signs and ranges of function values, the Pythagorean Identities
       and quotient identities.
  5.  right-triangle based definitions of the trigonometric functions, co functions, and
       trigonometric values of special angles.
  6.  reference angels, special angles as reference angles, and finding angle measures with
       special angles.
  7.  finding function values using a calculator.
  8.  finding angle measures using a calculator.
  9.  significant digits, solving triangles, dealing with angles of elevation or depression,
       and bearing.
10.  radian measure, converting between degrees and radians and finding function values
       for angles in radians.
11.  finding the arc length on a circle and the area of a sector of a circle.
12.  circular functions, finding values of circular functions, determining a number with a
       given circular function value, and applying circular functions.
13.  linear speed and angular speed.
14.  periodic functions, be able to graph the six trigonometric functions, and understand
       graphing techniques, amplitude and period.
15.  horizontal translations, vertical translations and combinations of translations.
16.  negative angle identities , fundamental identities, and using the fundamental identities.
17.  verifying identities by working with one side.
18.  the sum and difference identities for sine, cosine and tangent, and applying the sum
       and difference identities.
19.  double angle identities, product to sum and sum to product identities, half angle
       identities, and applying these identities.
20.  inverse functions and the inverse of the six trigonometric functions.
21.  solving trigonometric equations by linear models, factoring, quadratic formula, and
       using trigonometric identities.
22.  solving trigonometric equations with half angles and multiple angles.
23.  congruency and oblique triangles, the derivation of the law of sines, and solving
       SAA and ASA triangles along with finding the area of the triangle.
24.  the description of the ambiguous case, solving the SSA triangles, and analyzing data
       for possible number of triangles.
25.  the derivation of the law of cosines, solving SAS and SSS triangles, and using
       Heron’s formula for finding the area of a triangle.


1.  To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical
     methods to modeling and solving real-world situations.
2.  To represent and evaluate basic mathematical information verbally, numerically,
     graphically, and symbolically.
3.  To expand mathematical reasoning skills and formal logic in order to develop
     convincing mathematical arguments.
4.  To use appropriate technology to enhance mathematical thinking and understanding
     and to solve mathematical problems and judge the reasonableness of the results.
5.  To interpret mathematical models such as formulas, graphs, tables and schematics,
     and draw inferences from them.
6.  To recognize the limitations of mathematical and statistical models.
7.  To develop the view that mathematics is an evolving discipline interrelated with
      human culture, and to understand its connection to other disciplines.


                     Homework and participation in classroom discussion
                     Six tests including final (each equally weighted)
                     The Letter grade will be an ‘A’ if the average is between 90
                     and 100, a ‘B’ if between 80 and 89, a ‘C’ if between 70 and
                     79, a ‘D’ if between 60 and 69, and a ‘F’ if the average is below 60.

Syllabus statement on disabilities

Students with disabilities, including learning disabilities, who wish to request academic adjustments in this class should notify the Disability Services Office early in the semester so that the appropriate accommodations may be made.  In accordance with federal law, a student requesting academic adjustments must provide documentation of his/her disability to the Disability Services Counselor.  For more information, call or visit the Counseling Center at Cardenas North 103  (956) 882-8292 or e-mail

DISHONESTY/CHEATING: Students are expected to be above reproach in all scholastic activities.  Students who engage in scholastic dishonesty are subject to disciplinary penalties, including the possibility of failure in the course and dismissal from the university.  "Scholastic dishonesty includes but is not limited to cheating, plagiarism, collusion, the submission for credit of any work or materials that are attributable in whole or in part to another person, taking an examination for another person, any act designed to give unfair advantage to a student or the attempt to commit such acts."  Regents' Rules and Regulations, Series 50101, Section 2.2.
Since scholastic dishonesty harms the individual, all students, and the integrity of the university, policies on scholastic dishonesty will be strictly enforced.  (Refer to Student Reference Manual for more information)  Please take this warning seriously.

EMERGENCY POLICY STATEMENT:  In compliance with the Emergency UTB/TSC Academic Continuity Program, academic courses, partially or entirely, will be made available on the MyUTBTSC Blackboard course management system.  This allows faculty members and students to continue their teaching and learning via MyUTBTSC Blackboard ( in case the university shuts down as a result of a hurricane or any other natural disaster.

The university will use MyUTBTSC Blackboard to post announcements notifying faculty members and students of their responsibilities as a hurricane approaches our region.  If the university is forced to shut down, faculty will notify their students using Blackboard on how to proceed with their course(s).  To receive credit for a course, it is the student's responsibility to complete all the requirements for that course.  Failure to access course materials once reasonably possible can result in a reduction of your overall grade in the class.

To facilitate the completion of classes, most or all of the communication between students and the institution, the instructor, and fellow classmates will take place using the features in your MyUTBTSC Blackboard and UTB email system.  Therefore, all students must use Scorpion Online to provide a current email address.  Students may update their email address by following the link titled "Validate your e-Mail Account" in MyUTBTSC Blackboard Portal.  In the event of a disaster that disrupts normal operations, all students and faculty must make every effort to access an internet-enabled computer as often as possible to continue the learning process.

STUDENT ACADEMIC PROGRESS: UTB/TSC monitors academic progress every fall and spring semester to identify those students who are experiencing difficulty with their courses.  Satisfactory Academic Progress (SAP) is based upon two components:  GPA of 2.0 or higher and successful course completion of at least 70% of course work attempted.  Students remain in good standing with the university and Financial Aid when both criteria are met.  Students who do not maintain these required minimum standards will be placed on probation or suspension as appropriate.  The complete Satisfactory Academic Progress policy and the Undergraduate Satisfactory Academic Progress for Financial Aid policy can be found in the current Undergraduate Catalog.

Important Dates:

Mon. Aug 27

First day of classes


Nov. 21 – 23

Thanksgiving Holidays

Mon. Sept. 3

Labor Day Holiday


Sat. Dec 8     

Last day of classes

Fri. Oct. 19



Dec 10

Dead Day

Mon. Oct. 29 Deadline to withdraw with a "W"  

Dec  11 – 17   

Final examinations



 11:00 AM – 11:30 AM

 SET - B – 2.534


 8:45 AM – 9:15 AM

  SET - B – 2.534


10:45 AM – 11:30 AM

 SET - B – 2.534


1:15 PM – 1:30 PM

 SET - B – 2.534



The itinerary is subject to change at the discretion of the instructor.


© The University of Texas at Brownsville & Texas Southmost College
For comments or more information contact Fred W. Warnke.