TRIGONOMETRY
COURSE OVERVIEW

COURSE GOAL: To understand the trigonometric ratios as they are used in triangular and circular functions and to apply the concepts, principles and identity properties of trigonometry and algebra to solving problems.

COURSE OBJECTIVES: (Math Essential Academic Learning Requirements are in parentheses following each objective.) During this course the students will:

• Work with both arithmetic and geometric sequences. (1.3, 1.5, 2.1, 2.2, 2.3, 4.1)
• Identify series and use Sigma notation. (1.3, 1.5)
• Expand powers of binomials and use the General Expansion Formula. (1.5, 2.1, 2.2, 2.3)
• Use the trigonometric functions to solve right triangles and apply these skills to solving problems. (1.3, 1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 4.1, 5.1)
• Use the Law of Cosines and the Law of Sines to solve right triangles and problems. (1.3, 1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 5.1)
• Solve general triangles and apply the skills to solving problems. (1.3, 1.5, 5.1)
• Apply the triangle area formulas. (1.3, 1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 5.1)
• Use radian measure and define the circular functions. (1.3, 1.5, 5.1)
• Use periodicity and symmetry to graph the trigonometric functions. (1.3, 1.2, 1.5, 2.1, 4.1, 5.1)
• Simplify trigonometric functions and prove the trigonometric identities. (1.3, 1.5, 2.1, 4.1, 5.1)
• Use the trigonometric addition formulas and the double and half angle formulas to solve problems. (1.3, 1.5, 2.1, 2.3, 3.1, 3.2, 3.3, 4.1, 4.2, 5.1)
• Define and use vector operations to solve problems. (1.3, 1.5, 5.1)
• Define polar coordinates and graph polar equations. (1.3, 1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 5.1)
• Use the geometry of complex numbers. (1.3, 1.5)
• Evaluate expressions involving the inverse trigonometric functions. (1.3, 1.5, 5.1)
• Solve trigonometric equations and problems. (1.3, 1.5, 2.1, 2.2, 2.3, 3.1`, 3.2, 3.3, 4.1, 5.1)
• Define matrices and apply matrix terminology. (1.5, 4.1, 4.2, 4.3)
• Find sums and differences of matrices and products of scalars and matrices. (1.1, 1.5, 5.1)
•   Solve problems using matrices and solve systems of equations using inverses of matrices. (1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 5.1)
• use the properties of determinants to simplify an expansion and solve systems of equations using determinants. (1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 4.1, 5.1, 5.2)
• apply the fundamental counting principles to solving problems. (1.4, 1.5, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 4.1, 5.2, 5.2)
• find various permutations of sets of elements. (1.5, 5.1)
• determine the number of ways in which combinations of elements can be formed. (1.5, 2.1, 2.2, 2.3, 3.1)
• specify sample spaces and events for random experiments. (1.4, 1.5)
• find the probability that an event will occur. (1.4, 1.5, 4.1, 4.2, 4.3, 5.1, 5.2, 5.3)
• work with mutually exclusive and independent events. (1.4, 1.5, 5.1, 5.2, 5.3)
• recognize and characterize frequency distributions. (1.4, 1.5, 3.1)
• recognize and analyze normal distributions. (1.4, 1.5, 3.1, 3.2, 5.1, 5.2)

MATERIALS: textbook Algebra and Trigonometry, Structure and Method, Book 2, Houghton and Mifflin, teacher-prepared handouts and tests, adapted materials for visually impaired learners.

GRADING:

Attendance and daily assigned work:  50%

Class participation: 20%

Tests: 30%

Timeline: The text is divided six chapters (Chapters 11-16). Each chapter will require  4-5 weeks.

Chapter 11: (4-5 weeks) Sequences, series, formulas for the nth term of a series, Sigma notation, sums of series, infinite geometric series, powers of binomials, the General Binomial Expansion.

Chapter 12: (4-5 weeks) Angles and degree measure, trig. Functions of acute angles, trig. Functions of general angles, tables of trig. Functions, solving right triangles, Law of Cosines, Law of Sines, solving general triangles, areas of triangles.

Chapter 13: (4-5 weeks) Radian measure, circular functions, periodicity and symmetry, graphs of sine and cosine, graphs of the other trig. functions, the fundamental identities, addition formulas, double-angle and half-angle formulas, formulas involving the tangent.

Chapter 14: (4-5 weeks) Vector operations, vectors in the plane, polar coordinates, the geometry of complex numbers, De Moivre’s Theorem, the inverse sine and cosine, the other inverse functions, trigonometric equations.

Chapter 15: (4-5 weeks) Terminology of matrices, addition and Scalar multiplication, matrix multiplication, applications of matrices, determinants, inverses of matrices, expansion of determinants by minors, properties of determinants, Cramer’s Rule.

Chapter 16: (4-5 weeks) Fundamental counting principles, permutations, permutations with repeated elements, combinations, sample spaces and events, probability, mutually exclusive and independent events, frequency distributions, the normal distribution.

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