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General Information

Course ID (CB01A and CB01B)
MATHD032H
Course Title (CB02)
Precalculus II - HONORS
Course Credit Status
Credit - Degree Applicable
Effective Term
Fall 2024
Course Description
This course prepares students for calculus. Topics include extending the elementary functions of first-quarter precalculus to include the theory of periodic functions; composition of trigonometric functions with other elementary functions; polar co-ordinates; further exploration of the complex plane; introduction to the algebra of vectors. Because this is an honors course, students will be expected to complete extra assignments to gain deeper insight into precalculus.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This is a UC and CSU transferable course that meets a general education requirement for CSU GE and IGETC. It belongs on the °®¶¹´«Ã½ Liberal Arts A.A./A.S. degree. This is the second course in a sequence of two courses in precalculus mathematics intended to provide the student who has successfully completed intermediate algebra with the foundations needed for success in calculus and advanced courses in mathematics and the sciences. This part of the sequence emphasizes periodic functions. This course is the honors version of MATH 032. and as a result, includes more advanced assignments and assessments.

Foothill Equivalency

Does the course have a Foothill equivalent?
No
Foothill Course ID

Course Philosophy

Course Philosophy
This sequence of two courses in precalculus mathematics is intended to provide the student who has successfully completed intermediate algebra with the foundations needed for success in calculus and advanced courses in mathematics and the sciences. Throughout the sequence, the courses emphasize building analytical and quantitative skills and the mathematical maturity necessary for solving problems in mathematics and related fields. Specifically, the student will define variables and use them to write, analyze and graph functions and other relations which occur in modeling and other applications. The student will also develop skills in solving equations and inequalities. The material is rich in applications, both modern and classic, drawn from historical and multicultural origins of the topics and modern applications in many fields. Periodic functions are studied and used to model application problems in mathematics and science with an emphasis on developing analytical, numerical, graphical, and verbal skills as required. Trigonometry is approached from both the perspective of right-triangles and circular functions.

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Letter Grade
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Transferable to both UC and CSU
CSU GEArea(s)StatusDetails
CGB4CSU GE Area B4 - Mathematics/Quantitative ReasoningApproved
IGETCArea(s)StatusDetails
IG2XIGETC Area 2 - Mathematical Concepts and Quantitative ReasoningApproved

Units and Hours

Summary

Minimum Credit Units
5.0
Maximum Credit Units
5.0

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours5.010.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
60.0
Laboratory
0.0
Total
60.0
Course Out-of-Class Hours
Lecture
120.0
Laboratory
0.0
NA
0.0
Total
120.0

Prerequisite(s)

MATH D031. or MATH D031H (with a grade of C or better); or a satisfactory score on college placement

Corequisite(s)

Advisory(ies)

ESL D272. and ESL D273., or ESL D472. and ESL D473., or eligibility for EWRT D001A or EWRT D01AH or ESL D005.

Limitation(s) on Enrollment

  • (Not open to students with credit in the non-Honors related course.)
  • (Admission into this course requires consent of the Honors Program Coordinator.)

Entrance Skill(s)

General Course Statement(s)

(See general education pages for the requirements this course meets.)

Methods of Instruction

Lecture and visual aids

Discussion of assigned reading

Discussion and problem-solving performed in class

In-class exploration of internet sites

Quiz and examination review performed in class

Homework and extended projects

Guest speakers

Collaborative learning and small group exercises

Collaborative projects

Problem solving and exploration activities using applications software

Assignments

  1. Required readings from the text
  2. Problem-solving exercises, some including technology
  3. Exams and quizzes
  4. Optional project synthesizing various concepts and skills from the course content
  5. In addition, the honors project should include the completion of additional sets of advanced problems that require a deeper understanding of the topics and/or a written research report (10 to 15 pages). Note: The honors project will require 10 or more hours of work beyond the regular (non-honors) course requirements, and will include higher expectations for achievement in this more advanced work.

Methods of Evaluation

  1. Periodic quizzes and/or assignments from sources related to the topics listed in the curriculum are evaluated for completion and accuracy in order to assess students' comprehension and ability to communicate orally and in writing of course content and provide timely feedback to students on their progress.
  2. Projects (optional)

    Projects may be used to enhance the students' understanding of topics studied in the course in a group or individual formats where communicating their understanding orally through classroom presentation or in writing. The evaluation is to be based on completion and comprehension of course content and the students shall receive timely feedback on their progress.
  3. At least three one-hour exams without projects or at least two one-hour exams with projects are required. In these evaluations, the students are expected to provide complete and accurate solutions to problems that include both theory and applications by integrating methods and techniques studied in the course. Students shall receive timely feedback on their progress.
  4. One two-hour comprehensive final examination in which students are expected to display comprehension of course content and be able to choose methods and techniques appropriate to the various types of problems that cover course content. Students shall have access to the final exam for review with the instructor for a period determined by college and departmental rules.
  5. The honors project will be evaluated based on the depth of understanding and mastery of advanced techniques employed within the project.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • Graphing calculator and/or computer software
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
LarsonPrecalculus with LimitsCengage2022 / 5th edition
Barnett, Ziegler and Byleen. , 11th Edition. Wiley, 2012.Analytic Trigonometry with ApplicationsWiley2012 / 11th edition
Lial, Hornsby, Schneider and DanielsTrigonometryPearson2021 / 12th edition
Abramson, Jay, et al.PrecalculusOpenstax2021

Examples of Supporting Texts and References

AuthorTitlePublisher
Math Department Activity and Multicultural Resource Binder, available in the PSME Division Office
The Joy of Pi
The Crest of the Peacock: Non-European Roots of Mathematics
Geometry Civilized: History, Culture and Technique.
Trigonometric Delights
An Imaginary Tale: The Story of Sqrt(-1)
Historical Topics for the Mathematics Classroom
Multicultural Mathematics: Teaching Mathematics from a Global Perspective
Multiculturalism and Representation: Selected Essays
Multiculturalism in Mathematics, Science and Technology: Readings and Activities.
The MacTutor History of Mathematics Archive.
Trigonometry
Functions Modeling Change
Trigonometry, a Unit Circle Approach
Trigonometry, a Circular Function Approach.

Learning Outcomes and Objectives

Course Objectives

  • Evaluate the trigonometric function of an angle given in degree and radian measure
  • Identify special triangles and their related angle and side measures
  • Prove trigonometric identities
  • Graph the six basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs
  • Manipulate and simplify trigonometric expressions
  • Recognize the relationship between trigonometric functions and their inverses graphically and algebraically
  • Solve trigonometric equations, triangles, and applications
  • Define the polar coordinate system and introduce polar graphs
  • Examine complex numbers in the complex plane
  • Solve arc length and sector area problems
  • Examine the logic of conditional and bi-conditional statements as they appear in mathematical statements
  • Perform operations with 2-dimensional vectors
  • Apply trigonometric functions to model real-world applications
  • Develop and use sequences and series
  • Apply the theory and application of trigonometry through projects, extended reading, or programming and computational problems.

CSLOs

    Outline

    1. Evaluate the trigonometric function of an angle given in degree and radian measure
      1. Study angles, converting between radian and degree measures
      2. Use the unit circle and right triangles to define the six trigonometric functions
      3. Define and study properties of circular functions
      4. Use technology to evaluate trigonometric functions for any angle measured in radians or degrees
      5. Investigate applications such as, but not limited to
        1. Finding the angle formed by two hands of a clock
        2. Reflection and refraction of light
        3. Historical contributions in the development of the trigonometric functions by various cultures such as the Middle East, Europe, and India
    2. Identify special triangles and their related angle and side measures
      1. Identify the 30-60-90 triangle and corresponding side ratios
      2. Identify the 45-45-90 triangle and corresponding side ratios
      3. Find exact trigonometric function values of special angles
    3. Prove trigonometric identities
      1. Verify known trigonometric identities such as Pythagorean. Quotient, Reciprocal, Cofunction, Odd and Even, Sum and Difference, Double Angle and Half Angle Identities
      2. Use known trigonometric identities to verify other trigonometric identities
    4. Graph the six basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs
      1. Explore amplitude numerically, graphically, and symbolically
      2. Explore period numerically, graphically, and symbolically
      3. Explore vertical shifts and horizontal (phase) shifts numerically, graphically, and symbolically
      4. Develop the general form of trigonometric functions
    5. Manipulate and simplify trigonometric expressions
      1. Develop and use basic identities
        1. Pythagorean
        2. Quotient
        3. Reciprocal
        4. Cofunction
        5. Odd and even identities (negatives of angles)
      2. Develop and use other trigonometric identities
        1. Sum and difference of two angles
        2. Double angle
        3. Half angle
        4. Product to Sum (optional)
      3. Simplify trigonometric expressions
    6. Recognize the relationship between trigonometric functions and their inverses graphically and algebraically
      1. Define, evaluate, and graph the inverse trigonometric functions for sine, cosine, and tangent
      2. Define, evaluate, and graph the inverse trigonometric functions for cotangent, secant, and cosecant (optional)
      3. Determine domain and range
      4. Compose trigonometric and inverse trigonometric functions
      5. Establish inverse trigonometric identities
    7. Solve trigonometric equations, triangles, and applications
      1. Solve right triangles using trigonometric functions
        1. Solve for missing angles
        2. Solve for missing sides
      2. Apply the law of sines and the law of cosines to oblique triangles
        1. Solve for missing angles
        2. Solve for missing sides
      3. Investigate applications such as, but not limited to finding distances in problems arising in various applications from geometry, surveying, astronomy, physics, geography, navigation, and engineering
      4. Solve trigonometric equations
        1. Solve linear trigonometric equations
        2. Solve quadratic trigonometric equations
        3. Solve trigonometric equations involving multiples of angles
    8. Define the polar coordinate system and introduce polar graphs
      1. Plot points in the polar coordinate system
      2. Convert between polar and rectangular coordinates
      3. Convert between polar and rectangular equations
      4. Graph polar equations, functions, and relations
    9. Examine complex numbers in the complex plane
      1. Perform operations on complex numbers
      2. Graph complex numbers
      3. Write complex numbers in trigonometric/polar form
      4. Use DeMoivre's Theorem to find powers and roots
    10. Solve arc length and sector area problems
      1. Evaluate arc length
      2. Solve circular motion problems for angular and linear velocity
      3. Solve sector area problems
      4. Investigate applications such as, but not limited to
        1. Motion of objects, such as pulleys and gears
        2. Motion of planets
        3. British Nautical Mile
    11. Examine the logic of conditional and bi-conditional statements as they appear in mathematical statements
      1. Explore the relationships between a conditional statement and its converse, inverse, and contrapositive
      2. Explore the use of conditional and bi-conditional statements in mathematical statements, definitions, and theorems
    12. Perform operations with 2-dimensional vectors
      1. Study two-dimensional vectors geometrically
        1. Define and use vectors as directed line segments
        2. Compute the magnitude and direction of vectors
        3. Define and use standard unit vectors
        4. Represent displacement, velocity, etc. as vector quantities
      2. Study vector operations geometrically
        1. Define and use vector scalar multiplication
        2. Define and use vector addition
        3. Combine vectors geometrically using
          1. The triangular method
          2. The parallelogram method
      3. Study two-dimensional vectors algebraically
        1. Express vectors algebraically as the sum of scalar multiples of the standard unit vectors
        2. Express vectors using ordered pairs
        3. Identify horizontal and vertical vector and scalar components of a vector
        4. Add vectors using scalar components and compute resultant vectors
        5. Study properties of vector addition and scalar multiplication
      4. Study and use the dot product of two vectors
        1. Find the dot product of vectors
        2. Use the dot product to
          1. Find the magnitude of a vector
          2. Find the angle between two vectors
          3. Determine whether two vectors are orthogonal
        3. Study the properties of the dot product
        4. Find vector projections and resolve vectors into parallel and perpendicular vector components
      5. Application problems such as, but not limited to
        1. Static equilibrium problems
        2. Motion problems, such as sliding masses
        3. Work problems
        4. Historical development and use of vector quantities in solving problems in the sciences
    13. Apply trigonometric functions to model real-world applications
      1. Using periodic functions to model periodic phenomena such as temperature, electric current, simple harmonic motion (of a spring, for example), light and electromagnetic waves, water waves, the pressure of a plucked string
      2. Combining other functions with periodic functions to model phenomena such as damped harmonic motion
      3. Combining basic periodic functions to create other periodic functions; for example Fourier series
      4. Investigate applications such as, but not limited to, sound waves and the relationship of frequency to period, solving equations that arise from modeling periodic phenomena such as temperature, electric current, simple harmonic motion, light, and electromagnetic waves, water waves, pressure of a plucked string
    14. Develop and use sequences and series
      1. Examine sequences and series of real numbers
      2. Define arithmetic and geometric sequences and series and find an expression for their general terms
      3. Find the sum of finite arithmetic and geometric series
      4. Find the sum of infinite convergent geometric series
      5. Investigate application problems using arithmetic and geometric sequence and series such as, but not limited to
        1. Falling objects and projectiles
        2. Simple and compound interest, depreciation and annuities
        3. Historical development and use of sequence and series in solving problems in the sciences
    15. Apply the theory and application of trigonometry through projects, extended reading, or programming and computational problems.
      1. Typical problem-solving topics may include spherical trigonometry
      2. Typical applied projects may include any of the following:
        1. Details and history of the proofs for some of the main theorems in trigonometry.
        2. Applied projects in meteorology
        3. Applied projects in physics and structural engineering
        4. Applied projects in seismology
        5. Applied projects in sound engineering
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