Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Areas of Study | | MATH114 syllabus




COURSE NUMBER: MATH114
COURSE TITLE:Trigonometry
DIVISION:Sciences
IAI CODE(S): MTM 901
SEMESTER CREDIT HOURS:3
CONTACT HOURS:45
STUDENT ENGAGEMENT HOURS:135
DELIVERY MODE:In-Person

COURSE DESCRIPTION:
The study of the six trigonometric and circular functions, their inverses, the identities associated with these functions, the graphs associated with these functions, trigonometric equations and their applications. A graphing calculator is recommended.

PREREQUISITES:
Place into MATH114 with approved and documented math placement test scores or by completing MATH111 with a grade of C or better.

NOTES:

STUDENT LEARNING OUTCOMES:
Upon completion of this course, students will be able to:
  • Use, understand and write all trigonometric function symbolic forms and terminology, as well as the inverse trigonometric functions.
  • Clearly relate interpretations and solutions of trigonometric application problems.
  • Clearly demonstrate the organized, logical steps taken to arrive at the solution or verify an identity.
  • Master the use of a calculator and other relevant technology for evaluating/graphing trigonometric expressions or solving trigonometric/algebraic equations.
  • Achieve strong critical thinking/problem solving skills as applied to trigonometric problems.
Student learning outcomes (more detail):
  • Demonstrate knowledge of the definitions of the six trigonometric functions by calculating the missing parts of a right triangle using:
    • Any point (except the origin) on the terminal side of an angle in standard position.
    • Given lengths of any two sides.
    • Use, understand and write all trigonometric function symbolic forms and terminology, as well as the inverse trigonometric functions.
  • Demonstrate understanding of the six trigonometric functions by:
    • Evaluating trigonometric function values for specific acute, non-acute and quadrantal angles.
    • Using them to solve right triangle problems.
    • Using them to establish the eight fundamental identities.
  • Demonstrate comprehension of the eight fundamental trigonometric identities by:
    • Using them to verify:
      • General identities.
      • Cofunction identities.
      • Parity of the trigonometric functions.
      • Angle sum and difference identities.
      • Double-angle identities.
      • Half-angle identities.
      • Reference angle theorem.
      • Coterminal angle theorem.
    • Solving right triangle problems in abstractions and applications.
    • Solving trigonometric equations with single and multiple angles.
  • Demonstrate understanding of the radian measure of an angle by:
    • Converting radians to degrees and degrees to radians.
    • Applying it in calculating:
      • Arc length and area of a sector.
      • Linear and angular velocity.
    • Defining and evaluating the six circular functions.
  • Utilize traditional graphing methods, graphing calculators, and/or online graphing websites to:
    • Graph the six circular functions, including but not limited to their:
      • Vertical and horizontal translations.
      • Vertical and horizontal stretchings and shrinkings.
      • Reflections with the x axis.
    • Utilize calculators and/or computer software to calculate approximations for application problems.
    • Evaluating/graphing trigonometric expressions or solving trigonometric/algebraic equations.
    • Clearly demonstrate the organized, logical steps taken to arrive at the solution or verify an identity.
    • Achieve strong critical thinking/problem solving skills as applied to trigonometric problems.
    • Clearly related interpretations and solutions of trigonometric application problems.
  • Demonstrate comprehension of the inverse trigonometric functions by:
    • Defining them and their domains and ranges.
    • Utilizing them in solving trigonometric equations.
  • Solve oblique triangle problems using:
    • Law of sines, including the ambiguous case.
    • Law of cosines.
  • Utilize trigonometry to find the area of a triangle given:
    • Two sides and an included angle.
    • Two angles and an included side.
    • Three sides.

TOPICAL OUTLINE:
  • Geometric angle and triangle relationships [6%]
  • The six trigonometric functions of an angle in standard position with respect to a point on the terminal side of an angle [6%]
    • Defining functions
    • Evaluating functions and determining signs of each function.
    • Finding values of quadrantal angles
  • Fundamental identities [8%]
    • Reciprocal identities
    • Quotient identities
    • Pythagorean identities
    • Negative angle identities
    • Cofunction identities
  • The six trigonometric functions of acute angles in a right triangle [6%]
    • Defining functions in terms of an angle in a right triangle
    • Determining exact values of special acute angles and quadrantal angles
    • Evaluating trigonometric functions for non-acute angles by using reference angles and reference triangle.
  • Solving right triangles and applying to real world situations [6%]
  • Using calculator to find approximations [4%]
  • Radian measure and conversions between degrees and radians [4%]
  • The six circular functions [8%]
    • Defining the trigonometric functions in terms of real numbers
    • Evaluating circular functions
    • Applying radian measure: arc length, area of a sector, linear velocity, and angular velocity
  • Graphs of the six circular functions [20%]
    • Basic graphs of each function
    • Domain, range and period of each function
    • Techniques of graphing using reflection, stretching/shrinking, horizontal and vertical translations.
    • Using the graphing calculators and/or online graphing websites to graph the circular functions
  • Verifying identities [12%]
    • Techniques for verifying identities
    • Sum and difference identities
    • Double and half angle identities
    • Using special identities in problem solving
  • Inverse trigonometric functions [4%]
    • Defining inverse functions, their domains, ranges, and their graphs
    • Using inverse trigonometric functions to solve trigonometric equations
  • Solving oblique triangles [8%]
    • Law of sines
    • Law of cosines
  • Finding area of a triangle [8%]
  • Complex numbers (optional)
    • Operations with complex numbers (optional)
    • Trigonometric form of a complex number (optional)
    • Powers and quotients for a complex number and DeMoivre’s Theorem (optional)

TEXTBOOK / SPECIAL MATERIALS:

Trigonometry, 6th Edition, by McKeaque and Turner, Brooks/Cole-Thomson, 2008.
***Some instructors may use the 4th edition

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:

Quizzes and homework
Five- hour-long exams
Comprehensive final exam
Determination of grade is according to the following scale:

90%-100%
80%-89%
70%-79%
60%-69%
0%-59%
A
B
C
D
F
A grade of C is highly recommended before entering trig based Calculus or Physics.

BIBLIOGRAPHY:

STUDENT CONDUCT CODE:
Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

DISABILITY SERVICES:
Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

REVISION:
Spring 2019

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