Trigonometry
Scope and SequenceEdit
ObjectiveEdit
The goals in this trigonometry class will consist of first helping students develop a proficiency in advanced algebra and secondly demonstrating to students how algebra, when studied at an indepth level, naturally extends to more powerful mathematical concepts. Since trigonometry is an advanced high school math course, its study will require and build critical thinking skills by approaching problems in various ways. The methods used in problem-solving will involve the “rule of four” which consists of a numerical, graphical, analytical, and verbal approach. It is important that students develop rote skills but in a broader context that includes understanding topics conceptually.
Scope and SequenceEdit
The following is an outline of the topics covered in Trigonometry. An approximate number of days are allotted to the topics since the actual time varies depending upon the richness of class discussions that are generated. Furthermore, the textbook will be utilized as a resource but students will be held responsible for learning all material extensively taught in class. Tests are not generated based solely on problems found in the textbook but on the concepts discussed and developed in class. A minimum of two tests are given each 6 weeks.
Unit One (Approximate time 2 weeks)Edit
- Real Number System
- Properties of Algebra
- Evaluating/Simplifying Expressions
- Interval/Inequality/Set Notation
- Radical Expressions
- Factoring
Unit Two ( Approximate time 10 days)Edit
- More Factoring
- Simplifying Rational Expressions
- Solving Equations
Unit Three (Approximate time 9 days)Edit
- More Solving Equations
- Solving Inequalities
- Complex Numbers
Unit Four (Approximate time 7 days)Edit
- Graphing Linear Equations
- Slope of a Line
- Finding x and y intercepts
- Writing Linear Equations
- Writing Equations of Parallel and Perpendicular Lines
- Graphing Linear Inequalities
Unit Five (Approximate 17 days)Edit
- Identifying Functions
- Domain/Range
- Evaluating Functions
- Inverse Functions
- Piece-Wise Functions
- Continuity/Discontinuity
- Parent Functions
- Transformation of Parent Functions
Unit Six (Approximate 10 days)Edit
- Long Division/ Synthetic Division
- Graphing Rational Functions
- Polynomial Functions
- Critical Points and Extrema
Unit Seven (Approximate 4 days)Edit
- Remainder and Factor Theorem
- Rational Root Theorem
- Locating Zeros of a Polynomial
- Conics (only if time allows)
Unit Eight (Approximate 12 days)Edit
- Exponential Functions
- Logarithmic Functions
- Logarithmic Expressions
- Logarithmic Equations
- Applications
Unit NineEdit
- Right Triangles and Pythagorean Theorem
- Pythagorean Theorem and Special Right Triangles
- Applications of Pythagorean Theorem
- Solving Right Triangles using Trig Ratios
- Applications of Trig Ratios
Unit Ten- Circular Trig.Edit
- Angle measure in degree/radian
- Unit Circle
- Unwrapping the unit circle- 3 basic trig graphs
Unit Eleven-Graphs of circular trig. functionsEdit
- Amplitude, period, phase shift, domain/range
- Transformations of sine, cosine, tangent, cosecant, secant, and cotangent functions
Unit Twelve-inverse trig. functionsEdit
- Restricting domain/range to get inverse trig functions
- Finding the value of inverse trig functions
- Graphing inverse trig functions
Unit Thirteen- Fundamental trig. identitiesEdit
- Reciprocal Identities
- Quotient identities
- Pythagorean identities
- Proving trig identities
Unit Fourteen- Identities and solve trig. equationsEdit
- Sum/difference identities
- Double angle identities
- Half-angle identities
- Finding trig values using identities
- Solving trig equations using identities
Unit Fifteen-Law of cosine/sineEdit
- Solving Triangles
- Deriving Law of Sines
- The ambigous case for law of sines
- Law of cosines
Unit Sixteen-VectorsEdit
- Geometric Vectors
- Algebraic Vectors
- Vectors in 3-dimensional space
- Perpendicular vectors
- Applications of vectors
Unit Seventeen-Polar Coordinate SystemEdit
- Comparison of real plane, complex plane, and polar plane
- Polar coordinates
- Graphs of polar coordinates
- Polar and rectangular coordinates
- Polar form of complex numbers
- Products/Quotients of Complex Numbers
- Powers and Roots of Complex Numbers
Unit Eighteen-Parametric EquationsEdit
- Parameters, independent variables, dependent variables and functions
- Writing Parametric Equations
- Exploring Parametric Equations with graphing calculator
Unit Nineteen-Systems and MatricesEdit
- Circles
- Ellipses
- Hyperbolas
- Parabolas
- Transformations of Conics
- Systems of Equations
- Solving with Matrices
Unit Twenty- Sequences and SeriesEdit
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Infinite Sequences and Series
- Convergent and Divergent Series
- Sigma Notation and the nth term
- Binomial Theorem
- This outline is subject to change at the discretion of the instructor.
Trigonometry SyllabusEdit
Classroom ExpectationsEdit
- Be prompt
- Be prepared
- Be positive
- Be polite
- NO FOOD OR DRINK IN THE CLASSROOM
- NO CELLPHONE OR IPODS,ETC..
Materials NeededEdit
- Graphing Calculator TI-83+, TI-84
- Notebook (3-ring binder with pockets)
- Paper
- Pen/Pencil
Grading PolicyEdit
- Tests 55%
- Daily Grade 30%
- Final Exam 15%
A minimum of two tests will be given during a 6 –week period. Tests are not generated based solely on problems found in a math textbook and are given in various formats. Daily grades consist of homework, quizzes and so forth. Occasionally a project may be assigned and will count as a major test grade. Students are held responsible for learning extensively all material that is discussed and discovered in class. The math textbook is a resource to be utilized but examples and questions will be given at an indepth level.
- This syllabus is subject to change at the discretion of the instructor.
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