  
Student Learning Outcomes 
 Students will model, solve, and interpret applications using trigonometric functions, parametric and polar curves, and vectors.
 Students will solve triangles, trigonometric equations, and problems with vectors.
 Students will solve triangles, trigonometric equations, and problems with vectors.

Description  
 This course is a continuation of topics from MATH 48B. Topics include the six trigonometric functions, trigonometric identities, inverse trigonometric functions, trigonometric equations, right triangles, oblique triangles, vectors, parametric equations, and modeling data with various functions.


Course Objectives  
 The student will be able to:
 Analyze periodic functions using a graph and table of data.
 Investigate angles and aspects of a circle
 Define and analyze the geometric properties of the unit circle.
 Graph sine and cosine functions and model realworld data with trigonometric functions.
 Investigate other trigonometric functions
 Analyze inverse trigonometric functions
 Solve right triangles and oblique triangles
 Graph and analyze functions and relations expressed in polar coordinates and parametric equations
 Perform operations with 2D vectors.
 Apply trigonometric identities to simplify and evaluate trigonometric expressions and verify other identities
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (J) above
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Interpret mathematical solutions.

Special Facilities and/or Equipment  
  Graphing Calculator
 When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Analyze periodic functions using a graph and table of data.
 Determine if a realworld data set or graph is periodic
 Determine the period, midline, amplitude and frequency of a periodic function
 Extrapolate function values for a periodic function given in a graph or table
 Interpret amplitude, period, frequency, and shifts within the context of an application
 Investigate angles and aspects of a circle
 Study angles, converting between radian and degree measures
 Investigate relationship between arc length and radius of a circle
 Solve arc length and area of a sector problems
 Solve circular motion problems for angular and linear speed sector area problems
 Investigate the unit circle.
 Describe the relationship between the cosine and sine functions and the coordinates of a point on the unit circle
 Find exact trigonometric values for special angles
 Use reference angles to determine cosine and sine values
 Graph sine and cosine functions and model realworld data with trigonometric functions.
 Use the unit circle to construct the graphs of the sine and cosine functions
 Graph sine and cosine functions from equations and tables including transformations
 Solve trigonometric equations graphically
 Generate equations for sine and cosine functions from tables and graphs
 Use sine and cosine functions to model realworld data sets
 Investigate other trigonometric functions
 Define tangent, cotangent, secant and cosecant in terms of sine and cosine
 Examine graphs of tangent, cotangent, secant and cosecant functions
 Analyze the inverse trigonometric functions
 Define, evaluate, and graph the inverse trigonometric functions for sine, cosine, and tangent
 Determine the domain and range of a function and its inverse and investigate the relationship between them
 Recognize the relationship between the graph of a trigonometric function and its inverse
 Solve trigonometric equations algebraically, including equations of linear and quadratic types
 Compose trigonometric and inverse trigonometric functions
 Solve right triangles and oblique triangles
 Describe the six trigonometric ratios
 Use the appropriate trigonometric ratio to solve realworld problems involving right triangles
 Describe the relationships among the trigonometric ratios
 Develop the formula for the Law of Sines and Law of Cosines
 Apply the Law of Sines and Law of Cosines to realworld scenarios
 Graph and analyze functions and relations expressed in polar coordinates and parametric equations
 Graph and classify equations in polar coordinates
 Convert between polar and rectangular coordinates
 Describe the relationship between polar and rectangular coordinates using trigonometry
 Find parametric forms of plane curves
 Convert between equations in parametric form and rectangular form.
 Investigate application problems using parametric equations such as:
 Planetary motion
 Projectiles
 Perform operations with 2D vectors.
 Use vectors to model and solve realworld situations
 Determine the magnitude and direction of a vector
 Resolve a vector into components
 Add, subtract, and scale vectors graphically and algebraically
 Find the dot product of vectors
 Use dot product to find the magnitude of a vector
 Find the angle between two vectors
 Solve equations and systems of equations that arise when solving various problems involving vectors
 Investigate application problems using vectors such as:
 Static equilibrium problems
 Motion problems, such as sliding masses
 Apply trigonometric identities to simplify and evaluate trigonometric expressions and verify other identities
 Develop and use fundamental identities
 Pythagorean
 Quotient and Reciprocal
 Cofunction
 Odd and Even Identities
 Develop and use other trigonometric identities
 Sum and difference of two angles
 Sum to Product and Product to Sum identities
 Double Angle identities
 Simplify trigonometric expressions
 Verify trigonometric identities
 Investigate applications of trigonometric identities
 Solve equations using trigonometric identities
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (J) above
 Calculator/computer utilities for evaluating problems involving optimization
 Calculator/computer utilities for determining mathematical models using regression
 Calculator/computer utilities for finding intersection points for graphs of two functions
 Calculator/computer utilities for finding zeros or roots of functions
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Application problems from other disciplines
 Proper notation
 Interpret mathematical solutions.
 Explain the significance of solutions to application problems.

Methods of Evaluation  
  Homework
 Quizzes
 Exams
 Proctored Comprehensive Final Exam
 Class Participation
 Exploratory worksheets or labs
 Group projects

Representative Text(s)  
 Wilson, Adamson, Cox and O'Bryan, Precalculus: A Make It Real Approach, 1st Edition, Cengage Learning, 2013. Stewart, Redlin, and Watson, Precalculus: Mathematics for Calculus, 6th Edition, Cengage Learning, 2012.

Disciplines  
 Mathematics


Method of Instruction  
  Lecture
 Discussion
 Cooperative learning exercises


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: Homework problems covering subject matter from text and related material ranging from 30  60 problems per week. Students will need to employ critical thinking in order to complete assignments.
 Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
 Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB.
 Worksheets: Problems and activities covering the subject matter.
Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
