Course ID: MATH R117 Curriculum Committee Approval Date: 10/24/2018 Catalog Start Date: Fall 2019 COURSE OUTLINE OXNARD COLLEGE I. Course Identification and Justification: A. Proposed course id: MATH R117 Banner title: Precalculus & Trigonometry Full title: Precalculus and Trigonometry B. Reason(s) course is offered: This course is the prerequisite for Calculus at most four-year universities and fulfills lower division mathematics transfer admission requirements at most universities. This course was created to prepare students to succeed at Calculus. It is aligned with C-ID MATH 955. C. C-ID: 1. C-ID Descriptor: 2. C-ID Status: D. Co-listed as: Current: None II. Catalog Information: A. Units: Current: 6.00 B. Course Hours: 1. In-Class Contact Hours: Lecture: 105 Activity: 0 Lab: 0 2. Total In-Class Contact Hours: 105 3. Total Outside-of-Class Hours: 210 4. Total Student Learning Hours: 315 C. Prerequisites, Corequisites, Advisories, and Limitations on Enrollment: 1. Prerequisites Current: MATH R015: Beginning and Intermediate Algebra or MATH R014 or MATH R014B or MATH R033 or Placement as determined by the college's multiple measures assessment process. 2. Corequisites Current: 3. Advisories: Current: 4. Limitations on Enrollment: Current: D. Catalog description: Current: This course gives the calculus-bound student a solid foundation in precalculus algebra and analytic trigonometry, with emphasis on function concepts and graphing. Topics include equations and inequalities, analytic geometry of lines and conic sections, properties of functions, techniques of graphing, elementary functions (linear, quadratic, rational, exponential, logarithmic, and trigonometric) and inverse functions, trigonometric identities and equations, polar graphing, optimization applications, systems of equations, theory of equations, mathematical induction, binomial theorem, sequences, and series. E. Fees: Current: $ None F. Field trips: Current: Will be required: [ ] May be required: [ ] Will not be required: [X] G. Repeatability: Current: A - Not designed as repeatable H. Credit basis: Current: Letter Graded Only [ ] Pass/No Pass [ ] Student Option [X] I. Credit by exam: Current: Petitions may be granted: [ ] Petitions will not be granted: [X] III. Course Objectives: Upon successful completion of this course, the student should be able to: A. Graph functions and relations in rectangular coordinates and polar coordinates. B. Synthesize results from the graphs and/or equations of functions and relations. C. Apply transformations to the graphs of functions and relations. D. Recognize the relationship between functions and their inverses graphically and algebraically. E. Solve and apply equations including rational, linear, polynomial, exponential, absolute value, and logarithmic functions. F. Solve linear, nonlinear, and absolute value inequalities. G. Solve systems of equations and inequalities. H. Apply functions to model real world applications. I. Prove trigonometric identities. J. Identify special triangles and their related angle and side measures. K. Evaluate the trigonometric function at an angle whose measure is given in degrees and radians. L. Manipulate and simplify a trigonometric expression. M. Solve trigonometric equations. N. Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs. O. Evaluate and graph inverse trigonometric functions. P. Convert between polar and rectangular coordinates. Q. Calculate powers and roots of complex numbers using DeMoivre's Theorem. R. Represent a vector in the form and ai + bj IV. Student Learning Outcomes: A. Re-write and/or simplify algebraic and trigonometric expressions by using appropriate mathematical properties, identities, and substitutions. B. Solve polynomial, exponential, logarithmic, trigonometric, systems of equation and inequalities. V. Course Content: Topics to be covered include, but are not limited to: A. Coordinates, graphs, and inequalities 1. Rectangular Coordinates a. Finding the equation of a circle b. Given the equation, finding the center and radius c. Finding the midpoint and length of a line segment 2. Graphs and functions a. Identifying and sketching the 6 basic graphs of mathematics b. Finding the x- and y- intercepts of graphs 3. Equations of lines a. Finding the equation of a line having a specified geometric relationship with a curve b. Finding the slope of a line through two arbitrary points on curve 4. Symmetry and graphs a. Determining analytically if a graph possesses symmetry b. Graphing a set of points symmetric with respect to a given axis or line 5. Linear inequalities and absolute value inequalities a. Solving compound linear inequalities b. Solving absolute value inequalities 6. Quadratic and rational equations and inequalities a. Solving quadratic equations and inequalities b. Solving rational inequalities B. Functions 1. Definition of a function a. Stating the definition of a function and determining if a relation is a function b. Calculating using functional notation and computing quotients of the forms c. Algebraically finding the domain and range of a function 2. Graph of a function a. Calculating the average rate of change of a function b. Graphing functions with restricted domains or piecewise functions c. Calculating the instantaneous rate of change of a function by making up a table of values C. (optional) 1. Graphing curves using translation and reflection techniques 2. Combining functions a. Combining two functions using arithmetic operations b. Combining functions using composition c. Decomposing a function into two or more functions 3. Iteration (Optional) a. Performing iterations on a function b. Finding the fixed point of a function 4. Inverse functions a. Determining if two functions are inverses of each other b. Finding the equation of the inverse function c. Graphing the inverse function d. Applying the one-to-one concept to determine if a function has an inverse D. Polynomial and rational functions 1. Linear functions a. Formulating linear models to applications such as total cost, marginal cost, and depreciation b. Finding the equation of the regression line (optional) c. Computing iterations on a linear function (optional) 2. Graphs of quadratic functions a. Finding the vertex b. Finding the line of symmetry 3. Applied functions: applying function models to set up equations that optimize values for maximum/minimum problems 4. Graphing polynomial functions that are in factored form 5. Graphing rational functions that are in factored form E. Exponential and logarithmic functions 1. Introduction to exponential functions and their graphs a. Graphing functions of the form y = ax b. Solving simple exponential equations without using logarithms 2. The exponential function y = ex a. Graphing functions of the form y = ex + B + C b. Finding the domain, range, intercepts, and asymptote 3. Logarithmic functions and their properties a. Graphing logarithmic functions including y = a + ln(x - c) b. Rewriting a logarithmic expression using the change-of-base formula c. Solving exponential equations using logarithms d. Solving logarithmic equations using exponentials e. Finding the inverse of an exponential function f. Finding the inverse of a logarithmic function g. Simplifying logarithmic expressions using properties of logarithms F. The trigonometric functions 1. Radian measure a. Converting between degree and radian measure b. Solving problems involving angular speed, and arc length, and linear speed 2. Defining the trigonometric functions using unit circle and right triangle approaches 3. Simplifying expressions and calculating the trigonometric values of general angles using the reference angle concept G. Graphs of trigonometric functions 1. Trigonometric functions of real numbers a. Simplifying algebraic expressions using trigonometric substitutions b. Calculating sin0, cos0, given any trigonometric functions of 0 by using the Pythagorean identities 2. Graphing curves of the form y = Asin(Bx + C) + D and y = Acos(Bx + C) + D 3. Graphing the tangent and reciprocal functions H. Analytical trigonometry 1. Calculating trigonometric functions of opposite angles, double angles, half­ angles, and sums of angles 2. Solving trigonometric equations using radian and degree measure 3. Inverse trigonometric functions a. Graphing inverse trigonometric functions of y = arcsin x, y = arccos x, and y = arctan x b. Solving equations involving inverse trigonometric functions c. Calculating inverse trigonometric values such as arcsin (1/2) d. Calculating composition of trigonometric function with inverse trigonometric functions I. Additional topics in trigonometry 1. Right-triangle applications a. Resolving right triangles b. Solving application problems involving angle of elevation/depression c. Finding the area of a triangle using trigonometric formula 2. Resolving oblique triangles and solving applications using Law of Sines and Law of Cosines 3. Vectors in the plane, a geometric approach a. Calculating the sum of two vectors algebraically and illustrating the sum b. Calculating the horizontal and vertical components of a vector 4. Graphing equations given in parametric form 5. Polar coordinates a. Converting between rectangular and polar coordinates b. Converting equations between rectangular and polar form 6. Graphing polar curves J. Solving systems of equations using Gaussian Elimination, determinants and matrices 1. Solving nonlinear system of equations 2. Solving systems of inequalities (Optional) K. Analytic