COURSE: Math 1302 – Plane Trigonometry (3 – 3 – 0)

Summer I 2011 (CRN: 30038)

CATALOG DESCRIPTION: Trigonometric functions with an emphasis on fundamental identities, radian measure, graphing, inverse trigonometric functions, solving triangles and equations, vectors, and applications related to these topics.

(MATH 1316)

PREREQUISITE: A grade of “C” or better in MATH 1301 or placement by exam taken at UH-Downtown.

AUDIENCE: This is a freshman-level mathematics course, which requires a background consisting of one semester of college-level algebra. The course is primarily intended for majors in scientific and technical disciplines.

PURPOSE: This course provides the background in numerical and analytical trigonometry necessary for further study in college-level mathematics and its applications. The course may also be a prerequisite for certain science or technical courses, such as General Physics.

LEARNING OUTCOMES: At the completion of the course, the student should be able to:

1.	Define and graph the six trigonometric functions and their inverses.
2.	Find the trigonometric function values of certain special angles.
3.	State the eight fundamental trigonometric identities and use them to solve quadratic as well as basic trigonometric equations and prove other identities.
4.	Demonstrate familiarity with key advanced trigonometric identities.
5.	Use a calculator to evaluate trigonometric functions and round off as appropriate.
6.	Apply the trigonometric function definitions to solve right triangles.
7.	Apply the Law of Sines and the Law of Cosines to solve oblique triangles.
8.	Demonstrate an understanding of radian measure, its relation to degree measure, and its advantages in mathematical applications.
9.	Find a resultant vector and resolve a vector into horizontal and vertical vectors.
10.	Perform various other vector operations, such as scalar multiplication, finding the magnitude of a vector, finding the angle between two vectors, and the dot product.
11.	Write complex numbers in trigonometric form.
12.	Use DeMoivre's Theorem to compute powers of complex numbers.
13.	Compute roots of complex numbers.
14.	Solve various meaningful application problems.

TEXTBOOK: Trigonometry, Third Edition by M. Dugopolski, Addison-Wesley/Pearson Education Inc., Boston, Massachusetts, 2011.

METHOD OF EVALUATION: Departmental policy requires that:

1. A maximum of four and a minimum of three in-class tests and a comprehensive final exam must be given. The final exam must be taken by all students.

2. All major tests should be announced at least one week or the equivalent in advance.

3. The semester average of the grades is determined as follows:

Components	Percentage
4 midterm exams	50%
Homework	15%
Final exam	35%

4. The final course average will be used assign the final course grade according to the standard college formula:

90-100 à “A”

80-89 à “B”

70-79 à “C”

60-69 à “D”

0-59 à “F”

5. Neither an open book nor a take-home major test may be given.

6. An equivalent version of a test may not be distributed to students before a major test. Any review sheet should be comprehensive and the student should not feel that classroom notes, homework or the text may be ignored in favor of the review sheet.

Each student is expected to purchase or otherwise have access to a scientific calculator throughout the semester. The appropriate use of calculators should be taught and students should be allowed to use scientific calculators on the final exam. Graphing calculators are not required and the advanced features of a graphing calculator should not be used on any exam.

SUGGESTED METHODS: Since it is expected that students memorize the basic graphs of trigonometric functions, fundamental identities, and values of trigonometric functions for the special angles, it is suggested that instructors keep reminding students of these facts throughout the semester and assign enough problems for students to gain sufficient practice with these concepts. Students should be strongly encouraged to regularly study course material outside of class and to solve homework problems. Grading homework or giving frequent short quizzes on the homework may help enforce this. It is helpful in this class to solve meaningful application problems and state problems in context wherever possible. Within the stated course objectives, instructors may experiment with various methods and share their results with the department. Suggestions include: have students write explanations of answers and methods where possible; have students work in groups during class when appropriate; have students do activities with graphing calculators where appropriate. Classroom kits of graphing calculators are available from the department. In order to complete the course syllabus, it is vital that instructors not get delayed covering too many variations of certain problem types. In particular, instructors should not over-emphasize proving identities, solving triangles, or solving equations, at the expense of other topics in the course.

COURSE CONTENT:

UNITS WITH APPROXIMATE TIME

TEXT REFERENCE

Unit I – Angles and the Trigonometric Functions (9 hours)

Topics or techniques to be covered include: Angles and degree measure; radian measure and arc length; trigonometric functions; right triangle trigonometry; the fundamental identity and reference angles. Emphasis should be placed on the eight fundamental identities. Radian measure should be stressed for the remainder of the course, especially for graphing. Approximation and significant figures should be stressed in the applications throughout the course.

Sections 1.1, 1.2, 1.4 - 1.6

Unit II – Graphs of the Trigonometric Functions (6 hours)

Topics or techniques to be covered include: Unit circle and graphing; the general sine wave; graphs of the secant and cosecant functions; graphs of the tangent and cotangent functions.

Sections 2.1 - 2.4

Unit III – Trigonometric Identities (8 hours)

Topics or techniques to be covered include: Basic identities; verifying identities; sum and difference identities for cosine; sum and difference identities for sine and tangent; double-angle and half-angle identities; product and sum identities.

Sections 3.1 - 3.6

Unit IV – Solving Conditional Trigonometric Equations (7 hours)

Topics or techniques to be covered include: Inverse trigonometric functions; basic sine, cosine, and tangent equations; multiple angle equations; trigonometric equations of quadratic type.

Sections 4.1 - 4.4

UNIT V – Applications of Trigonometry (4 hours)

Topics or techniques to be covered include: The Law of Sines; the Law of Cosines; vectors.

Sections 5.1, 5.2, 5.4

UNIT VI - Complex Numbers (4 hours)

Topics or techniques to be covered include: Trigonometric form of complex numbers; powers and roots of complex numbers.

Sections 6.2 - 6.3

RESOURCE MATERIALS: Students enrolled in MATH 1302 at UH-D have access to the Math Lab in the Academic Support Center (925-N) where they may work with a tutor on understanding concepts or improving their skills. The Center is staffed with mathematics faculty and student assistants. The lab has tutorial assistance, videotapes, calculators, computer access for on-line homework assignments, and computer-aided drill on a walk-in basis. The Math Lab maintains extensive hours that are published each semester. Please encourage students to visit the Math Lab.

STATEMENT ON REASONABLE ACCOMMODATIONS: UHD adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with disabilities. Students with disabilities should be notified to register with Disabled Student Services and contact the instructor in a timely manner to arrange for appropriate accommodations.

Course Schedule:

This is the tentative course schedule. It will be updated during the proceeding of the course. You should check it regularly for the assignment due dates and exam dates. Although it will be updated in the best effort, any conflicts should be resolved according to the announcements made in the class.

Week\Day

Monday

Tuesday

Wednesday

Thursday

6/6

Prerequisites P.1, P.2, P.3, P.4

Section 1.1

6/7

Section 1.2

6/8

Section 1.4, 1.5

6/9

Section 1.6

Review

6/13

Section 2.1

Exam 1

6/14

Section 2.2, 2.3

6/15

Section 2.4

6/16

Section 3.1

Review

6/20

Section 3.2

Exam 2

6/21

Section 3.3, 3.4

6/22

Section 3.5, 3.6

6/23

Section 4.1

Review

6/27

Section 4.2

Exam 3

6/28

Section 4.3, 4.4

6/29

Section 5.1, 5.2

6/30

Section 5.4

Review

7/4

Independence Day

7/5

Section 6.2

Exam 4

7/6

Section 6.3

Review

7/7

Final Exam