COLLEGE OF THE DESERT

Size: px

Start display at page:

Download "COLLEGE OF THE DESERT"

Grace Lang
5 years ago
Views:

1 COLLEGE OF THE DESERT Course Code MATH-005 Course Outline of Record 1. Course Code: MATH a. Long Course Title: Trigonometry b. Short Course Title: TRIGONOMETRY 3. a. Catalog Course Description: This course is the first of a two semester sequence preparing students for Calculus. In this course, students will study functions with an emphasis on the trigonometric functions along with topics in analytic geometry. Topics will include a review of plane and coordinate geometry, functions including function notation, transformations and inverses, definitions and graphs of the trigonometric functions, modeling periodic behavior, solving triangle problems with the Law of Sines and Cosines, the conic sections, parametric equations and vectors. b. Class Schedule Course Description: This course is the first of a two semester sequence preparing students for Calculus. In this course, students will study functions with an emphasis on the trigonometric functions along with topics in analytic geometry. c. Semester Cycle (if applicable): N/A d. Name of Approved Program(s): LIBERAL ARTS with emphasis in Math and Science AA Degree and Transfer Preparation 4. Total Units: 5.00 Total Semester Hrs: Lecture Units: 5 Semester Lecture Hrs: Lab Units: 0 Semester Lab Hrs: 0 Class Size Maximum: 35 Allow Audit: No Repeatability No Repeats Allowed Justification 0 5. Prerequisite or Corequisite Courses or Advisories: Course with requisite(s) and/or advisory is required to complete Content Review Matrix (CCForm1-A) Prerequisite: MATH 040 Advisory: ENG 061 and Advisory: MATH Textbooks, Required Reading or Software: (List in APA or MLA format.) a. Stewart, J., Redlin, L., Watson, S (2012). Precalculus (7th /e). Cengage. ISBN: College Level: Yes Flesch-Kincaid reading level: Entrance Skills: Before entering the course students must be able: a. Interpret slope as a constant rate of change. MATH Interpret slope as a rate of change. b. Recognize when a table, graph, or equation is linear and create a linear model in the form of a table, graph, or equation. MATH Recognize when a table, graph, or equation is linear. c. Solve systems of equations. MATH Solve 2x2 and 3x3 systems of linear equations. d. Graph and find the equation of a circle. MATH Graph and find the equation of a circle. e. Solve quadratic equations by factoring, completing the square, taking square roots or the quadratic formula. MATH Solve quadratic equations by factoring, completing the square, taking square roots or the quadratic 05/02/ of 6

2 formula. f. Recognize when a table, graph, or equation is quadratic and create a quadratic model with a table, graph, or equation. MATH Create a quadratic model with a table, graph, or equation and solve maximum and minimum problems. g. Graph a parabola by finding the vertex, intercepts, and other symmetric points. MATH Graph a parabola by finding the vertex, intercepts, and other symmetric points. h. Demonstrate an understanding of the definition of a function including function notation and terminology (domain and range). MATH Apply the definition of a function including function notation and terminology (domain and range). i. Demonstrate an understanding that the key characteristic of an exponential function is its constant growth (decay) factor. MATH Comprehend that the key characteristic of an exponential function is its constant growth (decay) factor. j. Recognize and solve similar triangle problems. MATH Independently analyze and set up application problems, thus applying problem solving techniques to new situations. Also anticipate and check their proposed solutions. k. Basic knowledge about angles such as congruence of vertical angles theorem, familiarity with Pythagorean theorem. MATH Deduce right triangle side lengths using the Pythagorean Theorem and square roots. l. Demonstrate an understanding of and use deductive reasoning in the construction of a proof. MATH Acquire the principles of deductive thinking and relate in geometry and its applications. Advisory Skills: m. Demonstrate critical thinking skills when reading, and participating in class discussions. ENG Demonstrate the ability to think critically and express ideas using various patterns of development. n. Exhibit appropriate vocabulary and style. o. Demonstrate independent study skills and learning habits. p. Connect information gained from textbook readings and lectures to other disciplines. ENG Demonstrate the ability to use research skills including library resources such as books, periodicals, electronic databases and online resources such as the internet. ENG Demonstrate the ability to read and respond in writing beyond the literal interpretation of the text. 8. Course Content and Scope: Lecture: 1. Plane geometry review including facts and applications of angles, triangles, quadrilaterals and circles. 2. Deductive reasoning and proofs. 3. Functions including four ways of representing functions, function-notation, terminology, rates of change, and representing word problems with functions. 4. Transformations of functions. 5. The algebra of functions including the composition of functions. 6. One-to-one functions and inverse functions. 7. The trigonometric definitions using the right triangle and circular approach. 8. Solving triangles including right triangles, oblique triangles, Law of Sines, Law of Cosines, and applications. 9. Radian and degree measure including applications. 10. Trigonometric functions and their graphs, including phase shifts, amplitude, frequency, period, and translations. 11. Modeling periodic behavior using trigonometric functions. 12. Pythagorean Identities and using identities to deduce other identities. 13. Conic Sections including the characteristics of parabolas, circles, ellipses and hyperbolas in rectangular form, with graphing and applications. 14. Introduction to vectors. 05/02/ of 6

3 9. Lab: (if the "Lab Hours" is greater than zero this is required) Course Student Learning Outcomes: 1. Demonstrate that previously learned fundamental skills and knowledge from arithmetic, algebra, and geometry prior learning have been maintained or restored. 2. Demonstrate problem solving skills in application problems, with emphasis on the concepts of distance and angles. 3. Demonstrate problem solving skills in application problems, with an emphasis on periodic phenomena. 4. Create, analyze, and interpret graphs of trigonometric functions. 5. Develop an appreciation for the use of proof in mathematics, with an emphasis on its use in geometry, including the ability to create mathematical proofs of geometric properties. 10. Course Objectives: Upon completion of this course, students will be able to: a. Apply facts about angles, parallel lines and triangles to deduce further results about a geometric figure. b. Prove when two triangles are congruent or similar. c. Justify the lengths of sides in an isosceles right triangle and in a triangle. d. Deduce the lengths of sides in quadrilaterals such as trapezoids and rectangles using basic definitions, Pythagorean Theorem, perimeter and/or area. e. Calculate the measure of a central angle in a circle using the measure of the intercepted arc and calculate the areas of geometric figures involving circles. f. Apply facts about plane geometric figures to deduce the surface area and volume of three dimensional geometric figures. g. Demonstrate an understanding of the concept of a function by identifying and describing a function graphically, numerically and algebraically. h. Calculate the domain and range for a function expressed as a graph or an equation. From a graph, estimate the intervals where a function is increasing, decreasing and/or has a maximum or minimum value. i. Use and interpret function notation to find inputs and outputs from the graph, table and/or an equation describing a function j. From an equation, graph or table, calculate average rates of change by using a difference quotient or by using slopes of secant lines. Analyze average rates of change to determine the concavity of a graph. k. Demonstrate an understanding of the six basic transformations of functions by graphing translated functions including the quadratic functions. l. Represent a word problem (especially a geometric problem) with a function, including the use of functions to model real world applications. m. Determine when a function has an inverse (one to one functions) and find the inverse function graphically or algebraically. n. Form new functions through addition, subtraction, multiplication, division and composition. o. Recognize classical and analytic definitions of the trigonometric functions. Evaluate and/or estimate trigonometric function values at angles given in degree or radian measure. p. Solve triangles using right triangle trigonometry, the law of sines and the law of cosines. q. Convert from radian to degree measure and vice-versa. r. Graph the six trigonometric functions and demonstrate the ability to predict the corresponding graphic behavior of changes in parameters that modify amplitude, period, and phase. s. Use trigonometric functions to model periodic behavior. t. Use the basic Pythagorean identities to deduce further identities. u. Given the magnitude and direction of a vector in two-dimensional space, represent it in component form and ai+bj form. Also determine the magnitude and direction given the vector in ai+bj form. v. Perform basic arithmetic with vectors both graphically and via the use of the ai+bj form of the vectors. w. Analyze geometrically and manipulate algebraically the equations and graphs of the standard and shifted conic sections (as derived from their geometric definitions) including the major/minor axes, foci, directrix, and asymptotes in rectangular form. x. Analyze independently and set up application problems, thus applying problem solving technique to new situations. Demonstrate the ability to anticipate and check their proposed solutions. 05/02/ of 6

4 y. Communicate effectively with the instructor and mathematical community using proper terminology verbally as well as proper written notation. 11. Methods of Instruction: (Integration: Elements should validate parallel course outline elements) a. Demonstration, Repetition/Practice b. Discussion c. Lecture d. Technology-based instruction Other Methods: Calculator/Computer Demonstration 12. Assignments: (List samples of specific activities/assignments students are expected to complete both in and outside of class.) In Class Hours: Outside Class Hours: a. In-class Assignments 1. Attend classroom lectures and take notes. 2. Participate in classroom discussions to review, analyze, diagnose and evaluation various methods of solution used on their homework. 3. Complete assigned lab activities. Activities include problem solving, and exercises to improve skills and mathematical understanding. 13. b. Out-of-class Assignments 1. Read textbooks and supplementary assignments. 2. Complete daily assigned homework. Problems include problem solving, and exercises to improve skills and mathematical understanding. 3. Complete examinations involving problems that apply studied principles to new situations. Methods of Evaluating Student Progress: The student will demonstrate proficiency by: College level or pre-collegiate essays Written homework Guided/unguided journals Portfolios Term or research papers Reading reports Computational/problem solving evaluations Presentations/student demonstration observations Group activity participation/observation Product/project development evaluation True/false/multiple choice examinations Mid-term and final evaluations Student participation/contribution Student preparation 14. Methods of Evaluating: Additional Assessment Information: Chapter tests with in-class essay type exam questions, additional assignments as per the direction of the instructor and a comprehensive final exam with essay questions. Assignments and exams involve both performing computational problems and applying skills and ideas to new situations. 05/02/ of 6

5 15. Need/Purpose/Rationale -- All courses must meet one or more CCC missions. CSU GE Area B: Physical and its Life Forms(mark all that apply) B4 - Mathematics/Quantitative Thinking PO-GE C4.b - Language & Rationality (Communication & Analytical Thinking) Gather, assess, and interpret relevant information. Apply logical and critical thinking to solve problems; explain conclusions; and evaluate, support, or critique the thinking of others. IO - Scientific Inquiry Analyze quantitative and qualitative information to make decisions, judgments, and pose questions. IO - Global Citizenship - Scientific & Technological Literacy Utilize quantitative expression in a variety of contexts. These would include units of measurement, visual representations, and scales and distributions. Synthesize, interpret, and infer, utilizing information, data, and experience to solve problems, innovate, and explore solutions. 16. Comparable Transfer Course University System Campus Course Number Course Title Catalog Year CSU CSU Los Angeles MATH 104B Precalculus: Trigonometry Special Materials and/or Equipment Required of Students: 18. Materials Fees: Required Material? Material or Item Cost Per Unit Total Cost 19. Provide Reasons for the Substantial Modifications or New Course: SLO Update 20. a. Cross-Listed Course (Enter Course Code): N/A b. Replacement Course (Enter original Course Code): N/A 21. Grading Method (choose one): Letter Grade Only 22. MIS Course Data Elements a. Course Control Number [CB00]: CCC b. T.O.P. Code [CB03]: Mathematics, General c. Credit Status [CB04]: D - Credit - Degree Applicable d. Course Transfer Status [CB05]: B = Transfer CSU e. Basic Skills Status [CB08]: 2N = Not basic skills course f. Vocational Status [CB09]: Not Occupational g. Course Classification [CB11]: Y - Credit Course h. Special Class Status [CB13]: N - Not Special i. Course CAN Code [CB14]: N/A j. Course Prior to College Level [CB21]: Y = Not Applicable k. Course Noncredit Category [CB22]: Y - Not Applicable l. Funding Agency Category [CB23]: Y = Not Applicable m. Program Status [CB24]: 1 = Program Applicable Name of Approved Program (if program-applicable): LIBERAL ARTS with emphasis in Math and Science Attach listings of Degree and/or Certificate Programs showing this course as a required or a restricted elective.) 05/02/ of 6

6 23. Enrollment - Estimate Enrollment First Year: 0 Third Year: Resources - Faculty - Discipline and Other Qualifications: a. Sufficient Faculty Resources: Yes b. If No, list number of FTE needed to offer this course: N/A 25. Additional Equipment and/or Supplies Needed and Source of Funding. N/A 26. Additional Construction or Modification of Existing Classroom Space Needed. (Explain:) N/A 27. FOR NEW OR SUBSTANTIALLY MODIFIED COURSES Library and/or Learning Resources Present in the Collection are Sufficient to Meet the Need of the Students Enrolled in the Course: Yes 28. Originator Daniel, P Kleinfelter Origination Date 10/19/17 05/02/ of 6

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in