syllabus

Syllabus

Syllabus for College Trigonometry

Spring 2020

I. Course Information: MATH 131 College Trigonometry (3 credits)

II. Semester and Year: Spring 2020

III. Instructor Contact Information: Gary Leiter

Email: cia.leiter@gmail.com or text me at: 805-801-8055

V. Course Description: Prerequisites: A grade of at least a “C” in College Algebra or Intermediate Algebra or Algebra II

This course covers Trigonometric functions, equations, and identities, geometric properties of acute and right triangles, radian and circular functions, trigonometry applications and vectors, complex numbers, polar and parametric equations, and exponential and logarithmic functions

VI. Course Objectives:

The main objective of College Trigonometry is for students to learn and apply the fundamentals of trigonometric laws.

VII. Student Outcomes:

Upon successful completion of the course, students should be able to:

1. Recognize and construct angles with measures given in degrees or radians,

convert between radians and degrees, determine reference angles, and apply

angle measurement to problems.

2. Define trigonometric functions in terms of the lengths of the sides of right

triangles and apply to problems involving right triangles.

3. Evaluate trigonometric functions of special angles by utilizing geometric

properties of triangles.

4. Define and evaluate trigonometric functions as circular functions.

5. Analyze and describe the graphs of trigonometric functions and their algebraic

representations in terms of their properties, including the phase shift, the period,

vertical shifts, the amplitude, asymptotes, and the domain and range.

6. Define, evaluate, describe, and graph inverse trigonometric functions including

their domains and ranges.

7. Derive and prove fundamental trigonometric identities including the Pythagorean

identities, the reciprocal identities, the sum and difference identities, and apply

these to derive more general identities.

8. Solve trigonometric and inverse trigonometric equations.

9. Apply the Pythagorean Theorem, the law of sines, and the law of cosines to solve

right and oblique triangles, and application problems.

10. Apply the definitions of trigonometric functions to describe vector quantities in

terms of their components and in terms of their magnitudes and directions.

11. Apply vector algebra to problems involving vector quantities such as force,

velocity and displacement.

12. Perform arithmetic operations on complex numbers using both standard and

trigonometric form, including applications involving De Moivres Theorem, and

interpret those operations geometrically.

VIII. Required Texts:

Lial, M., Hornsby, J., Schneider, D. Trigonometry 8th Edition. Boston: Pearson, Addison Wesley, 2005.

Technology

Students are required to have a scientific calculator in class regularly.

Other Ideas Integrated Into The Course

Students will be assigned problem-solving exercises included in the text in each lesson designed to be done in groups, discussed, and increase graphing calculator skills. Students will also be assigned exercises called “Extending the Ideas” designed to encourage students to go “beyond the text” and experiment with ideas and results to come up with conclusions.

IX. Class Participation:

Students are expected to ask relevant questions, read the material assigned, complete homework and exams. The assignments must be turned in on time for full credit.

X. Course Requirements and Evaluation Criteria

Evaluation Tools:

Homework assignments (41 lessons)

205 points (approx 10%)

Chapter Quizzes

500 points (approx 25%)

Chapter Exams and Final

1200 points (approx 65%)

Total Points Available

1905 points

XII. Student Attendance:

Online and in-class attendance is expected by regularly submitting homework and taking exams. It is your responsibility to withdraw from the class if it is not working out for you. If you do not withdraw and fail to complete work in a timely manner, a grade of “F” will be assigned.

**If you plan on taking the class seriously as part of your college accomplishments, please step up and do the work and do your best. This is your reputation as a student that is being compromised if you do not.

XII. Required Written Work:

Homework must be turned in on or before due date for full credit. I expect you to work with classmates on homework assignments and ask me pertinent questions so that you can be successful in the class. Late work will result in a grade reduction of 10% per day late. WORK SUBMITTED MORE THAN ONE WEEK AFTER THE DUE DATE WILL NOT BE ACCEPTED. Please don't ask.

XIII. Plagiarism: Cheating and or plagiarism will result in a grade of “F” for the quiz/exam and/or assignment.

XIV. Grading Scale:

A 90-100%

B 80-89

C 70-79

D 60-69

F 0-59

XV. Schedule of Lecture Topics and Assignments:

Unit #1--Jan 7-11

Chapter 1: Trigonometric Functions

Angles

Angle relationships and similar triangles

Trigonometric functions

Unit #2—Jan 14-18

Chapter 1 continued

Using the definitions of the trigonometric functions

Chapter 2: Acute Angles and Right Triangles

Trigonometric functions of acute angles

Trigonometric functions of non-acute angles

Finding trigonometric function values using a calculator

Unit #3—Jan 21-25

Chapter 2 continued

Solving right triangles

Further applications of right triangles

Unit #4—Jan 28-Feb 1

Chapter 3; Radian Measure and Circular Functions

Radian measure

Applications of radian measure

The unit circle and circular functions

Unit #5—Feb 4-8

Chapter 3 continued

Linear and angular speed

Chapter 4; Graphs of the Circular Functions

Graphs of the sine and cosine functions

Translations of the graphs of the sine and cosine functions

Unit #6—Feb 11-15

Chapter 4 continued

Graphs of the other circular functions

Harmonic motion

Chapter 5; Trigonometric Functions

Fundamental identities

Unit #7—Feb 18-22

Chapter 5 continued

Verifying trigonometric identities

Sum and difference identities for cosine

Sum and difference identities for sine and tangent

Unit #8—Feb 25-Mar 1

Chapter 5 continued

Double-angle identities

Half-angle identities

Chapter 6; inverse Circular Functions and Trigonometric Equations

Inverse circular functions

Unit #9—Mar 4-8

Chapter 6 continued

Trigonometric equations part 1

Trigonometric equations part 2

Equations involving inverse trigonometric functions

Unit #10—Mar 18-22

Chapter 7; Applications of Trigonometry and Vectors

Oblique triangles and the law of sines

The ambiguous case of the law of sines

The law of cosines

Unit #11—Mar 25-29

Chapter 7 continued

Vectors, operations, and the dot product

Applications of vectors

Chapter 8; Complex Numbers, Polar Equations, and Parametric Equations

Complex numbers

Unit #12—April 1-5

Chapter 8 continued

Trigonometric (polar) form of complex numbers

The product and quotient theorems

De Moivre’s theorem; powers and roots of complex numbers

Unit #13—April 8-12

Chapter 8 continued

Polar equations and graphs

Parametric equations, graphs, and applications

Unit #14—April 15-19

Chapter 9; Exponential and Logarithmic Functions

Exponential functions

Logarithmic functions

Evaluating logarithms; equations and applications

Unit #15—April 22-26

Finals Week