Trigonometry Syllabus

Angel Website:  http://pcps.myelearning.org/frameIndex.htm
Angela Schmit's Website:  http://manila.esu4.org/angelaschmit/

Course Syllabus

Description of Course

Prerequisites

• Algebra II (one full academic year)

The Objectives of the Course 

• Provide a strong foundation of precalculus concepts, techniques, and applications to prepare students for more advanced work
• Place appropriate emphasis on discrete mathematics and data analysis--subjects that provide the mathematical framework for many important contemporary applications
• Show how technology can be used as a tool to facilitate learning and doing mathematics
• Present topics in a way that encourages students to become actively involved and accommodate different learning and teaching styles
• Develop quantitative reasoning and problem-solving skills
• Develop abilities to understand and communicate mathematical ideas effectively
• Increase appreciation of mathematics through seeing a wide range of mathematical applications

Texts

Explanation of Instruction

• Lecture and discussion every day.
• Quizzes every two or three lessons.
• Tests after every unit.
• Spelling/Writing assignments as needed.
• Angel Website--On-Line Learning
  

Visual Aids, Utilized Films, Film Strips, Etc.

• Marker board
• Calculators (Texas Instruments--TI 83, TI 85, and TI 92) provided by the school district
• Computer Software/Technology
• Supplementary Workbooks

Units and Contents

Chapter 1:  Linear and Quadratic Functions

• Points and Lines
  To find the intersection of two lines and to find the length and midpoint of a segment
  
• Slopes of Lines
  To find the slope of a line and to determine whether two lines are parallel, perpendicular, or neither
  
• Finding Equations of Lines
  To find an equation of a line given certain geometric properties of the line
  
• Linear Functions and Models
  To model real-world situations by means of linear functions
  
• The Complex Numbers
  To add, subtract, multiply, and divide complex numbers
  
• Solving Quadratic Equations
  To define and graph quadratic functions
  
• Quadratic Functions and Their Graphs
  To model real-world situations using quadratic functions
  

Chapter 2:  Polynomial Functions

• Polynomials
  To identify a polynomial function, to evaluate it using synthetic substitution, and to determine its zeros.
• Synthetic Division; The Remainder and Factor Theorems
  To use synthetic division and to apply the remainder and factor theorems
• Graphing Polynomial Functions
  To graph a polynomial function and to determine an equation for a polynomial graph
• Finding Maximums and Minimums of Polynomial Functions
  To write a polynomial function for a given situation and to find the maximum and minimum value of the function
• Using Technology to Approximate Roots of Polynomial Equations
  To use technology to approximate the real roots of polynomial equations
• Solving Polynomial Equations by Factoring
  To solve polynomial equations by various methods of factoring, including the use of the rational root theorem
• General Results for Polynomial Equations
  To apply general theorems about polynomial equations
  

Chapter 3:  Inequalities

• Linear Inequalities; Absolute Value
  To solve and graph linear inequalities in one variable
• Polynomial Inequalities in One Variable
  To solve and graph polynomial inequalities in one variable
• Polynomial Inequalities in Two Variables
  To graph polynomial inequalities in two variables and to graph the solution set of a system of inequalities
• Linear Programming
  To solve certain applied problems using linear programming
  
  Chapter 4:  Functions
  
  
• Functions
  To identify a function, to determine the domain, range, and zeros of a function, and to graph a function
• Operations on Functions
  To perform operations on functions and to determine the domains of the resulting functions
• Reflecting Graphs; Symmetry
  To reflect graphs and to use symmetry to sketch graphs
• Periodic Functions; Stretching and Translating Graphs
  To determine periodicity and ampitude from graphs, to stretch and shrink graphs both vertically and horizontally and to translate graphs
• Inverse Functions
  To find the inverse of a function, if the inverse exists
• Functions of Two Variables
  To graph functions of two variables in a two-dimensional coordinate system and to read such graphs
  
• Forming Functions from Verbal Descriptions
  To form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function
  

Chapter 5:  Exponents and Logarithms

• Growth and Decay: Integral Exponents
  To define and apply integral exponents
• Growth and Decay:  Rational Exponents
  To define and apply rational exponents
• Exponential Functions
  To define and use exponential functions
• The Number e and the Function e^x
  To define and apply the natural exponential function
• Logarithmic Functions
  To define and apply logarithmic functions
• Laws of Logarithms
  To prove and apply laws of logarithms
• Exponential Functions; Changing Bases
  To solve exponential equations and to change logarithms from one base to another
  

Chapter 6:  Analytic Geometry

• Coordinate Proofs
  To prove theorems from geometry by using coordinates
  
• Equations of Circles
  To find equations of circles and to find the coordinates of any points where circles and lines meet.
• Ellipses
  To find equations of ellipses and to graph them
• Hyperbolas
  To find equations of hyperbolas and to graph them
• Parabolas
  To find equations of parabolas and to graph them
• Systems of Second-Degree Equations
  To solve systems of second-degree equations
• A New Look at Conic Sections
  To define conic sections in terms of eccentricity and to classify the graph of a second-degree equation by examining the coefficients in the equation
  

Chapter 7:  Trigonometric Functions

• Measurement of Angles
  To find the measure of an angle in either degrees or radians and to find coterminal angles
• Sectors of Circles
  To find the arc length and area of a sector of a circle and to solve problems involving apparent size
• The Sine and Cosine Functions
  To use the definitions of sine and cosine to find values of these functions and to solve simple trigonometric equations
• Evaluating and Graphing Sine and Cosine
  To use reference angles, calculators or tables, and special angles to find values of the sine and cosine functions and to sketch the graphs of these functions
• The Other Trigonometric Functions
  To find values of the tangent, cotangent, secant, and cosecant functions and to sketch the functions' graphs
• The Inverse Trigonometric Functions
  To find values of the inverse trigonometric functions
  

Chapter 8:  Trigonometric Equations and Applications

• Simple Trigonometric Equations
  To solve simple trigonometric equations and to apply them
• Sine and Cosine Curves
  To find equations of different sine and cosine curves and to apply these equations
• Modeling Periodic Behavior
  To use trigonometric functions to model periodic behavior
• Relationships Among the Functions
  To simplify trigonometric expressions and to prove trigonometric identities
• Solving More Difficult Trigonometric Equations
  To use trigonometric identities or technology to solve more difficult trigonometric equations
  

Chapter 9:  Triangle Trigonometry

• Solving Right Triangles
  To use trigonometry to find unknown sides or angles of a right triangle
• The Area of a Triangle
  To find the area of a triangle given the lengths of two sides and the measure of the included angle
• The Law of Sines
  To use the law of sines to find unknown parts of a triangle
• The Law of Cosines
  To use the law of cosines to find unknown parts of a triangle
• Applications of Trigonometry to Navigation and Surveying
  To use trigonometry to solve navigation and surveying problems
  

Chapter 10:  Trigonometric Addition Formulas

• Formulas for sin (alpha +/- beta) and cos (alpha +/- beta) 
  To derive and apply formulas for sin (alpha +/-  beta) and cos (alpha +/- beta) 
• Formulas for tan (alpha +/- beta)
  To derive and apply formulas for tan (alpha +/- beta)
• Double-Angle and Half-Angle Formulas
  To derive and apply double-angle and half-angle formulas
• Solving Trigonometric Equations
  To use identities to solve trigonometric equations
  

Chapter 11:  Polar Coordinates and Complex Numbers

• Polar Coordinates and Graphs
  To graph polar equations
  
• Geometric Representation of Complex Numbers
  To write complex numbers in polar form and to find products in polar form
  
• Powers of Complex Numbers
  To use De Moivre's theorem to find powers of complex numbers
  
• Roots of Complex Numbers
  To find roots of complex numbers
  

Chapter 12:  Vectors and Determinants

• Geometric Representation of Vectors
  To perform basic operations on vectors
  
• Algebraic Representation of Vectors
  To use coordinates to perform vector operations
  
• Vector and Parametric Equations:  Motion in a Plane
  To use vector and parametric equations to describe motion in the plane
  
• Parallel and Perpendicular Vectors; Dot Product
  To define and apply the dot product
  
• Vectors in Three Dimensions
  To extend vectors to three dimensions and to apply them
  
• Vectors and Planes
  To sketch planes and to find equations of planes
  
• Determinants
  To define and evaluate determinants
• Applications of Determinants
  To use determinants to solve algebraic and geometric problems
  
• Determinants and Vectors in Three Dimensions
  To define and apply the cross product
  

Chapter 13:  Sequences and Series

• Arithmetic and Geometric Sequences
  To identify an arithmetic or geometric sequence and find a formula for its nth term
  
• Recursive Definitions
  To use sequences defined recursively to solve problems
  
• Arithmetic and Geometric Series and Their Sums
  To find the sum of the first n terms of arithmetic or geometric series
  
• Limits of Infinite Sequences
  To find or estimate the limit of an infinite sequence or to determine that the limit does not exist
  
• Sums of Infinite Series
  To find the sum of an infinite geometric series
  
• Sigma Notation
  To represent series using sigma notation
  
• Mathematical Induction
  To use mathematical induction to prove that a statement is true
  

Chapter 14:  Matrices

• Matrix Addition and Scalar Multiplication
  To find the sum, difference, or scalar multiples of matrices
• Matrix Multiplication
  To find the product of two matrices
• Applying Matrices to Linear Systems
  To find the inverse of a 2 x 2 matrix and to solve linear systems using matrices
• Communication Matrices
  To solve communication network problems using matrices
• Transition Matrices
  To make predictions using powers of matrices
• Transformation Matrices
  To find the images of points under different types of transformations using matrices
  

Chapter 15:  Combinatorics

• Venn Diagrams
  To use venn diagrams to illustrate intersections and unions of sets and to use the inclusion-exclusion principle of solve counting problems invvolving intersections and unions of sets
  
• The Multiplication, Addition, and Complement Principles
  To use the mulitiplication, addition, and complement principles to solve counting problems
  
• Permutations and Combinations
  To solve problems involving permutations and combinations
  
• Permutations with Repetition; Circular Permutations
  To solve counting problems that involve permutations with repetition and circular permutations
  
• The Binomial Theorem; Pascal's Triangle
  To use the binomial theorem and Pascal's triangle
  

Chapter 16:  Probability

• Introduction to Probability
  To find a sample space of an experiment and the probability of an event or either of two events
  
• Probability of Events Occurring Together
  To find the probability of events occurring together and to determine whether two events are independent
  
• The Binomial Probability Theorem
  To use the binomial probability theorem to find the probability of a given outcome on repeated independent trials of a binomial experiment and to approximate the probability when the trials are not independent
  
• Probability Problems Solved with Combinations
  To use combinations to solve probability problems
  
• Working with Conditional Probability
  To solve problems involving conditional probability
  
• Expected Value
  To find expected value in situations involving gains and losses and to determine whether a game is fair
  

Chapter 17:  Statistics

• Tables, Graphs, and Averages
  To display a set of data using various statistical graphs and to find the mean, median, and mode
  
• Box-and-Whisker Plots
  To draw a box-and-whisker plot for a set of data and to use box-and-whisker and stem-and-leaf plots to compare sets of data
  
• Variability
  To find the variance and standard deviation of a set of data and to convert data to standard values
  
• The Normal Distribution
  To recognize various types of distributions, to determine for a normal distribution the percent of data withing a given interval, and to find percentiles
  
• Sampling
  To recognize different types of sampling procedures, to identify their limitations, and to estimate population characteristics based on samples
  
• Confidence Intervals for Surveys and Polls
  To use a sample proportion to find a confidence interval for a corresponding population proportion
  

Chapter 18:  Curve Fitting and Models

• Introduction to Curve Fitting; the Least-Squares Line
  To find the line of best fit for a set of data and to find the correlation coefficient for a set of data
  
• Fitting Exponential Curves
  To find an exponential function that models certain sets of data
  
• Fitting Power Curves
  To fit a power curve to a set of data
  
• Choosing the Best Model
  To choose a model that best describes a set of data
  

Chapter 19:  Limits, Series, and Iterated Functions

• Limits of Functions
  To find the limit of a function or the quotient of two functions and to determine whether a function is continuous
  
• Graphs of Rational Functions
  To sketch the graph of a rational function
  
• Using Technology to Approximate the Area Under a Curve
  To use technology to approximate the area under a curve
  
• Power Series
  To use the power series of a given function to find an infinite series for a functional value or for a related function
  
• Analyzing Orbits
  To analyze orbits for iterations of a given function
  
• Applications of Iterated Functions
  To use iterated functions to model money and population growth
  

Chapter 20:  Introduction to Calculus

• The Slope of a Curve
  To find derivatives of functions
  
• Using Derivatives in Curve Sketching
  To sketch the graphs of functions using derivatives
  
• Extreme Value Problems
  To solve extreme value problems using derivatives
  
• Velocity and Acceleration
  To find instantaneous velocities and accelerations
  

This Page was last update: Wednesday, January 20, 2010 at 7:59:00 PM
This page was originally posted: 5/31/2006; 2:15:06 PM.
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