Plane Trigonometry
MATHEMATICS DEPARTMENT
Houston Community College-Southeast
Chuen Huang, Ph.D.
Phone 713.718.7150
E-mail: chuen.huang@hccs.edu
Math 1316 Plane Trigonometry
CRN 61910
Course Syllabus and Outline
Catalog Description: MATH 1316 Plane Trigonometry. Topics include solutions of triangles, Euler
identity, graphing of trigonometric and inverse trigonometric functions, identities, trigonometric equations,
applications including DeMoivre’s Theorem, and an introduction to vector analysis. Prerequisite: MATH
1314 or the equivalent. (Plane geometry is recommended). 3 credit (3 lecture).
Prerequisites: A grade of C or better in Math 1314 or the equivalent.
Course Intent: This course is intended for students whose curriculum requires trigonometry as a
prerequisite for higher mathematics courses. It may also be taken as a first course in trigonometry or as a
review course. Students whose curricula are generally non-technical in nature may take this course as a
mathematics elective if the necessary algebraic and geometric prerequisites have been met. The
transferability of this course as either mathematics credit or elective credit is at the discretion of the school
to which the student intends to transfer.
Audience: This course is for students who need trigonometry in order to prepare for higher mathematics
courses.
Course Objectives: Upon completion of this course, a student should be able to:
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Recognize the six basic trigonometric functions and understand the relationships between them.
Evaluate the trigonometric functions of special angles.
Find reference or related angles and coterminal angles.
Use a calculator or a table (not on exams) to find trigonometric function values of any angle.
Solve right triangles.
Convert degrees to radians and vice-versa.
Solve problems dealing with the application of radian measures.
Solve problems relating to linear and angular velocities.
Recognize the graphs of the six basic trigonometric functions.
Know the amplitude, period, and phase shift for sine and cosine functions.
Sketch functions exhibiting the above properties.
Recognize the various identities including sum and difference angle formula, double angle formula, and half angle
formulas.
Prove trigonometric identities using the formulas given above.
Solve trigonometric equations and inverse trigonometric equations.
Solve triangles using the sine and cosine laws.
Find areas of triangles.
Rewrite a complex number in polar form.
Use DeMoivre’s Theorem to simplify a complex number raised to a whole number exponent.
Find the nth root of a complex number.
Solve problems dealing with vectors.
Plane Trigonometry − Course Outline
Math 1316
Page 2 of 6 Pages
Revised: April of 2007
21. Recognize polar graphs.
Textbook: Dugopolski, Mark, Trigonometry, Addison-Wesley, Second Edition, 2007.
Course Outline: Instructors may find it preferable to cover the course topics in the order listed below.
However, Instructor may choose to organize topics in any order, but all material must be covered.
Advising Times: M , W 8:30 am- 9 am, 1- 1:30 pm, T, R 8-9 am ESID 1026
CHAPTER
Approximate Time
Section Numbers
Chapter 1 Angles and the Trigonometric Functions
Topics
(8.5 hours)
Topics to be covered include: angles, degree measure, radian measure, angle
relationships, similar triangle, definitions of trigonometric functions, reference angles,
problem solving, and the fundamental identity.
1.1
Angles and Degree Measure
1 hour
1.2
Radian Measure, Arc Length, and Area
1 hour
1.3
Angular and Linear Velocity
1 hour
1.4
The Trigonometric Functions
1 hour
1.5
Right Triangle Trigonometry
2 hours
1.6
The Fundamental Identity and Reference Angles
1 hour
Recommend Examination 1
1.5 hours
Chapter 2 Graphs of the Trigonometric Functions
(6.5 hours)
Topics to be covered include: graphs of the trigonometric functions.
2.1
The Unit Circle and Graphing
2 hours
2.2
The General Sine Wave
1 hour
2.3
Graphs of the Secant and Cosecant Functions
1 hour
2.4
Graphs of the Tangent and Cotangent Functions
1 hour
2.5
Combining Functions (Optional)
Chapter 3 Trigonometric Identities
2.5 hours
(8.5 hours)
Topics to be covered include: coverage of fundamental trigonometric identities,
verification of trigonometric identities, and identities involving multiple angles. The
chapter concludes with a discussion of how to obtain the trigonometric function of
products as sums.
3.1
Basic Identities
2 hours
3.2
Verifying Identities
2 hours
3.3
Sum and Difference Identities for Cosine
1 hour
Plane Trigonometry − Course Outline
Math 1316
Page 3 of 6 Pages
Revised: April of 2007
3.4
Sum and Difference Identities for Sine and Tangent
1 hour
3.5
Double-Angle and Half-Angle Identities
1 hour
3.6
Product and Sum Identities (Optional)
1.5 hours
CHAPTER
Approximate Time
Section Numbers
Chapter 4 Solving Conditional Trigonometric Equations
Topics
(7.5 hours)
Topics to be covered include: complex numbers, trigonometric form of complex numbers
the product and the quotient of complex numbers, powers and roots of complex numbers,
and equations with complex solutions. The unit concludes with the use of DeMoivre’s
theorem to find roots to an equation.
4.1
The Inverse Trigonometric Functions
2 hours
4.2
Basic Sine, Cosine, and Tangent Equations
2 hours
4.3
Multiple Angle Equations
1 hour
4.4
Trigonometric Equations of Quadratic Type
1 hour
Recommend Examination 2
1.5 hours
Chapter 5 Applications of Trigonometry
(8 hours)
Topics to be covered include: Law of Sines, Law of Cosines, and Area. This unit
concludes with vectors in a two-dimensional plane.
5.1
The Law of Sines
2 hours
5.2
The Law of Cosines
2 hours
5.3
Area of a Triangle
1 hour
5.4
Vectors
2 hours
5.5
Applications of Vectors
1 hour
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Chapter 6 Complex Numbers, Polar Coordinates, and
Parametric Equations
(8.5 hours)
Topics to be covered include: complex numbers, trigonometric form of complex numbers,
the product and the quotient of complex numbers, powers and roots of complex numbers,
equations with complex solutions, and working with polar coordinates. This unit
concludes with graphing in the polar coordinate plane.
6.1
Complex numbers
1 hour
Plane Trigonometry − Course Outline
Math 1316
Page 4 of 6 Pages
Revised: April of 2007
6.2
Trigonometric Form of Complex Numbers
1 hour
6.3
Powers and Roots of Complex Numbers
3 hours
6.4
Polar Equations
2 hours
Recommend Examination 3
1.5 hours
Final Examination: Tuesday, May 10, 2011, 11 am.
Departmental Policies:
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Each instructor must cover all course topics by the end of the semester. The final exam is
comprehensive and questions on it can deal with any of the course objectives.
Each student should receive a copy of the instructor’s student syllabus for the course during the first
week of class.
A minimum of three in class tests and a comprehensive final departmental examination must be given.
The final examination must betaken by all students.
All major tests should be announced at least one week or the equivalent in advance.
The final exam must count for at least 25 to 40 percent of the final grade.
The final course average will be used in the usual manner (90-100 “A”; 80-89 “B”; 70-79 “C”;
60-69 “D”; Below 60 “F”).
Either an open book or a take home major test may be given at the discretion of the instructor.
Any review sheet should be comprehensive and the student should not feel that classroom notes,
homework and tests may be ignored in favor of the review sheet for any examination.
Resource Materials: Any student enrolled in Math 1316 at HCCS has access to the Academic Support
Center where they may get additional help in understanding the theory or in improving their skills. The
Center is staffed with mathematics faculty and student assistants, and offers tutorial help, video tapes and
computer-assisted drills. Also available is a student’s Solutions manual which may be obtained from the
Bookstore.
Suggested Methods: It is helpful to begin each class with questions related to the material discussed and
assigned homework problems. In presenting new material, it is suggested that an explanation be followed
by students working examples in class. Students should be encouraged to work the review exercises at the
end of each chapter. Students should be encouraged to visit the Academic Support Center at their
respective colleges.
Americans with Disabilities Act (ADA): Students with Disabilities: Any student with a documented
disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the Disability Services Office at the respective college at the beginning
of each semester
Plane Trigonometry − Course Outline
Math 1316
Page 5 of 6 Pages
Revised: April of 2007
1. (NEW) Withdrawals:
The Texas State Legislature has begun to impose penalties on students who drop courses
excessively. In 2207, the Legislature passed a law limiting students to no more than six
(6) total course withdrawals throughout their academic career in obtaining a
baccalaureate degree. To help students avoid having to drop/withdraw from any class,
HCC has instituted an Early Alert process by which you instructor will "alert" you and
HCC student services of the chance you might fail a class because of excessive absences
and/or poor academic performance. You should visit with your instructor, a counselor,
or HCC Online Student Services to learn about your options.
Students MUST visit with a faculty advisor, a counselor or online student services prior
to withdrawal from class. If a withdrawal is to be given, this must be done prior to
November 8, 2007 at 4:30pm. After that date and time, students will no longer be
allowed to drop and will receive the grade that they earned. Faculty will NO longer be
allowed to give Ws on the final grade sheet; any faculty member who wishes to withdraw
a student will be required to process the drop BEFORE November 8, at 4:30.
2. (NEW) Online Tutoring Services
Houston Community College offers FREE online tutoring in a variety of subjects, including
mathematics, English and writing. To take advantage of these Online Tutoring Services, go to
www.hccs.askonline.net. Your questions will be answered by a qualified HCC tutor or faculty
member within 24 hours (usually under 6 hours).
3. Student Course Reinstatement Policy
Students have a responsibility to arrange payment for their classes when they register, either through cash,
credit card, financial aid, or the installment plan. Faculty members have a responsibility to check their class
rolls regularly, especially during the early weeks of a term, and reconcile the official class roll to ensure that
no one is attending class whose name does not appear on it. Students who are dropped from their courses
for nonpayment of tuition and fees who request reinstatement after the official date of record payment of
tuition and fees who request reinstatement after the official date of record (OE Date) can be reinstated by
making payment in full and paying an additional $75 per course reinstatement fee. A student requesting
reinstatement should present the registrar with a completed Enrollment Authorization Form with the
signature of the instructor, department chair, or dean who should verify that the student has been regularly
attending class. Students who are reinstated are responsible for all course policies and procedures, including
attendance requirements. A dean may waive the reinstatement fee upon determination that the student was
Plane Trigonometry − Course Outline
Math 1316
Page 6 of 6 Pages
Revised: April of 2007
dropped because of a college error. The dean should note the nature of the error in a memo to the registrar
with appropriate documentation.
4. (NEW) Students with Disabilities:
"Any student with a documented disability (e.g. physical, learning, psychiatric, developmental, vision,
hearing, etc.) who needs to arrange reasonable accommodations must contact the Disability Support
Services (DSS) Counselor at the beginning of each semester. Faculty members are authorized to provide
only the accommodations requested by the DSS office. Mr. Chris Caldwell is the Interim Southeast
College's DSS Counselor. His telephone number is (713) 718-7218."