ࡱ> LhKi bjbj.. I?DbDbV(((((<<<8tDL<q/l(,,,.......$14/(/((,,+/c c c (,(,.c .c c z+-,_v>,.A/0q/N,)5)5 --^)5(p-lc //q/)5B :  GROSSMONT COLLEGE COURSE OUTLINE OF RECORD Curriculum Committee Approval: 04/26/2022 GCCCD Governing Board Approval: 06/14/2022 MATHEMATICS 170 ANALYTIC TRIGONOMETRY 1. Course Number Course Title Semester Units MATH 170 Analytic Trigonometry 3 Semester Hours 3 hours lecture: 48-54 hours 96-108 outside-of-class hours 144-162 total hours 2. Course Prerequisites A C grade or higher or Pass in Mathematics 108 or 110 or equivalent or appropriate placement beyond intermediate algebra. Note: Mathematics 103 is not equivalent to Mathematics 110 Corequisite None Recommended Preparation None 3. Catalog Description A theoretical approach to the study of the trigonometric functions with emphasis upon circular functions, trigonometric identities, trigonometric equations, graphical methods, inverse functions, vectors and applications, complex numbers, and solving triangles with applications. Passing both MATH 170 and MATH 175 is equivalent to passing MATH 176. A student will earn a total of 7 units for passing both MATH 170 and MATH 175. A student will only earn 6 units if they pass both MATH 170 and MATH 176. 4. Course Objectives The student will: a. Illustrate trigonometric functions such as phase shift, amplitude (if applicable), principal Domain and inverse function. b. Demonstrate the ability to use arc lengths and radian measure in dealing with the trigonometric functions. c. Solve trigonometric equations and identities. d. Solve vector, right triangle, and oblique triangle problems, and graphing of the trigonometric functions and their variations. 5. Instructional Facilities Standard classroom 6. Special Materials Required of Student Graphing calculator. 7. Course Content a. Preliminary Concepts A Review: Angles, properties of circles-chords, central angles measuring arclengths, properties of 30 degree-60 degrees and 45 degree right triangles, rectangular coordinate system-distance and symmetry, functions and relations. Paths and wrapping functions, periodic functions. Introduction to unit circle and its reference points. c. Cosine and Sine: Reduction identities using symmetry, trigonometric tables and interpolation, graphs of sine and cosine identifying amplitude, period, phase shifts and reflections, sums of functions and basic trigonometric equations. d. Trigonometric identities and trigonometric equations for real numbers. e. Tangent function: Definition, graph, identities and equations. f. Trigonometric Functions of Angle Measure: Degrees and radian measure for angles: the six trigonometric functions defined, applications of 30 degree-60 degrees and 45 degree right triangles, reduction identities, tables, graphs. g. Trigonometric identities and equations for angles. h. Inverse Trigonometric Functions: Principal values, inverse of functions, inverse of trigonometric expressions. i. Complex Numbers: Rectangular and polar form, roots. j. Introduce contributions from a diverse group of mathematicians relevant to the content of the course. k. Application problems relevant to current events and students lived experiences. 8. Method of Instruction Employ a variety of teaching methods, including lectures, instructor presented examples, student-led discussions, collaborative learning, think-pair-share, formative assessments (e.g. exit slips), and multimedia presentations. These instructional techniques strive to include students lived experiences and different cultural and historical perspectives 9. Methods of Evaluating Student Performance Homework. Independent exploration activities such as modeling traveling or standing waves. Class participation/problem presentations. Quizzes, chapter exams, and an in-class comprehensive final exam. 10. Outside Class Assignments a. Homework. b. Take-home projects such as projectile motion using parametric equations c. Problem sets. 11. Representative Texts a. Representative Text(s): 1) Lial, Margaret, John Hornsby, and David Schneider. Trigonometry. Boston, MA: Pearson, 2021 2) Stewart, James, Lothar Redlin, Saleem Watson. Precalculus, Mathematics for Calculus. Boston, MA: Cengage Learning, 2016. b. Supplementary texts and workbooks: None Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Categorize trigonometric problems and use appropriate theorems, formulas, and algorithms to solve them. Use the appropriate technology to solve problems requiring trigonometry. Formulate, analyze, and differentiate trigonometric functions numerically, graphically, and symbolically and have the ability to transition between these representations. Communicate the mathematical process and assess the validity of the solution.   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