Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
√ TRIGONOMETRY Mathematics Prince George’s County Public Schools SY 2011-2012 Course Code: 370003 Prerequisites: Algebra 2 Credits: 1.0 Math, Merit Trigonometry is a preparation for Pre-Calculus. Topics covered include introduction to the six trigonometric functions, working with trigonometric functions to solve problems involving right and non-right triangles, circular functions, trigonometric identities and exploring algebraic and geometric interpretations of the graphs of the trigonometric functions. INTRODUCTION: Typically in a Math class, to understand the majority of the information it is necessary to continuously practice your skills. This requires a tremendous amount of effort on the student’s part. Each student should expect to dedicate 2 - 3 hours of studying for every hour in class. Some hints for success in a Math class include: attending class daily, asking questions in class, and thoroughly completing all the homework problems with detailed solutions as soon as possible after each class session. INSTRUCTOR INFORMATION: Name: Mrs. Ligaya Laureta E-Mail: [email protected] Planning: 3A & 4B Phone: 301-449-4800 Ext 435 CLASS INFORMATION: COURSE NUMBER: CLASSES MEET: Every other day for 90 minutes for 4A, 1B & 3B ROOM: 226 TEXT: Trigonometry by Lial, Hornsby and Schneider WEB SITE: www.ictcm.org CALCULATORS The use of a graphing calculator is required. While participants may use any graphing calculator, the instruction in the course requires the TI-83. The TI-84 is very similar and can be used as well. Knowledge and competence for use of other graphing calculators will be the sole responsibility of the student. GRADING: Your grade will be computed from the following categories: class work, homework, and assessment. The following weighted average will be used to calculate your grade. Category Brief Description Grade Percentage CLASS WORK/ THIS INCLUDES ALL WORK COMPLETED IN THE CLASSROOM SETTING. INCLUDING: NOTEBOOKS , WARM-UPS, VOCABULARYWRITTEN RESPONSES TO CONSTRUCTED RESPONSES (BCR/ECR) WHERE APPLICABLE, GROUP DISCUSSION, ACTIVE PARTICIPATION IN MATH PROJECTS, COMPLETION OF ASSIGNMENTS 30% THIS INCLUDES ALL WORK COMPLETED OUTSIDE THE CLASSROOM TO BE GRADED ON ITS COMPLETION AND STUDENT’S PREPARATION FOR CLASS (MATERIALS, SUPPLIES, ETC.) ASSIGNMENTS CAN INCLUDE, BUT NOT LIMITED TO: PROBLEM OF THE WEEK, FRIDAY NIGHT HOMEWORK THIS CATEGORY ENTAILS BOTH THE TRADITIONAL (EXAMS AND QUIZZES) AND ALTERNATIVE (PRESENTATIONS, PROJECTS, PORTFOLIOS) METHODS OF ASSESSING STUDENT LEARNING. EXAMS, QUIZZES, PORTFOLIOS, RESEARCH/UNIT PROJECTS, ORAL PRESENTATIONS SUGGESTED CRITERIA FOR GRADING PRESENTATIONS, PROJECTS, PORTFOLIOS: CONCEPTS/OBJECTIVES HAVE BEEN MET COMPLETION OF PROJECT CREATIVITY, ORIGINALITY 20% GROUP PARTICIPATION HOMEWORK ASSESSMENT 50% Your grade will be determined using the following scale: 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69% D 59% and below E SAT/ACT: SAT/ ACT preparation is infused into daily instruction. The curriculum is embedded with standardized test preparation activities and test-taking strategies that will help students be successful on high-stakes tests like the SAT, ACT or college entrance exams. The practice in each lesson will prepare the students for the format as well as for the content. IMPORTANT DATES: First Day of School Professional Development ½ Day Professional Development End of 1st Quarter (45 days) Grading/Teacher Planning Parent/Teacher Conferences End of 2nd Quarter (46 days) Grading/Teacher Planning Day ½ Day Professional Development Professional Development End of 3rd Quarter (46 days) Grading/Teacher Planning Last Day for Students (44 days) Last Day for Teachers Monday, August 23, 2010 Friday, September 24, 2010 Thursday, October 14, 2010 Friday, October 29, 2010 Monday, November 1, 2010 Friday, November 12, 2010 Friday, January 21, 2011 Monday, January 24, 2011 Friday, February 18, 2011 Friday, March 4, 2011 Thursday, March 31, 2011 Friday, April 1, 2011 Monday, June 13, 2011 Tuesday, June 14, 2011 First Quarter at a Glance Throughout first quarter students will apply Algebra and Geometry Concepts in finding Angle measures, solving for Reference angles, coterminal angles and quadrantal angles. This quarter lays the foundation of the entire course. Students will learn about Trigonometric Functions and Identities. They shall be able to find function values of angles. By the end of First Quarter Trigonometry students should be able to: Angles Review the basics Algebra and Geometry Concepts Define basic Terminologies Find Degree Measure Define Standard Position Find Coterminal Angles Find the Complement and Supplement of an Angle Find measures of Complementary and Supplementary Angles Calculate with Degrees, Minutes, Converting between Decimal Degrees and Degrees, Minutes, and Seconds Quadrantal Angles Angle Relationships and Similar Triangles Review Geometric Properties Define Vertical Angles Find Angle Measures Apply Angle Sum of a Triangle Enumerate the Types of Triangles Find Angle Measures in Similar Triangles Trigonometric Functions Review Square Roots and Rationalizing Find Function Values of an Angle Find Function Values of Quadrantal Angles Summarize Undefined Function Values Using the Definitions of the Trigonometric Functions Enumerate Reciprocal Identities Determine Signs and Ranges of Function Values Enumerate Pythagorean Identities Enumerate Quotient Identities Trigonometric Functions of Acute Angles Determine the Right-Triangle-Based Definitions of the Trigonometric Functions Find Cofunctions Find Trigonometric Function Values of Special Angles Find Reference Angles Express Special Angles as Reference Angles Find Angle Measures with Special Angles Find Function Values Using a Calculator Find Angle Values Using a Calculator Second Quarter at a Glance Throughout second quarter students will solve Right Triangles and apply this to solving problems related to Angles of Elevation and Depression, and Bearing. Students will also convert angle measures from Radian to Degree, and vice versa; Linear and Angular measure. In addition, students will be introduced to the graph the Circular Functions and learn to translate their graphs. By the end of Second Quarter Trigonometry students should be able to: Solving Right Triangles Determine Significant Digits Solve Triangles Solve problems related to Angles of Elevation or Depression Solve problems related to Bearing Radian Measure Define Radian Measure Convert Between Degrees and Radians Find Function Values for Angles in Radians Applications of Radian Measure Find the Arc Length on a Circle Find the Area of a Sector of a Sector The Unit Circle and the Circular Functions Define Circular Functions Find Values of Circular Functions Determine a Number with a given Circular Function Value Apply Circular Functions Linear and Angular Speed Define Linear Speed Define Angular Speed Convert from Linear Speed to Angular Speed Graphs of the Sine and Cosine Functions Define Periodic Graphs Graph the Sine Function Graph the Cosine Function Apply Graphing Techniques, Amplitude, and Period Use Trigonometric Model Translations of the Graphs of the Sine and Cosine Functions Identify Horizontal Translations Identify Vertical Translations Graph Combinations of Translations Determine a Trigonometric Model using Curve Fitting Graphs of the Tangent and Cotangent Functions Graph of the Tangent Function Graph the Cotangent Function Apply Graphing Techniques Graphs of the Secant and Cosecant Functions Graph the Secant Function Graph the Cosecant Function Apply Graphing Techniques Apply Addition of Ordinates Connect Graphs with Equations Third Quarter at a Glance Throughout third quarter students will work on Trigonometric Identities: Fundamental, Sum and Difference, Double-Angle, HalfAngle. They shall verify Trigonometric Identities. In addition, students will be introduced to Inverse circular functions and Trigonometric Equations. By the end of Third Quarter Trigonometry students should be able to: Fundamental Identities Use Fundamental Identities Use the Fundamental Identities Verifying Trigonometric Identities Verify Identities by working with One Side Verify Identities by working with Both Sides Sum and Difference Identities for Cosine Identify the Difference Identity for Cosine Identify the Sum Identity for Cosine Identify the Cofunction Identities Apply the Sum and Difference Identities Sum and Difference Identities for Sine and Tangent Identify the Sum and Difference for Sine Identify the Sum and Difference for Cosine Apply the Sum and Difference Identities Double Angle Identities Enumerate the Double-Angle Identities Apply the Double-Angle Identities Half Angle Identities * Identify the Half-Angle Identities Apply the Half-Angle Identities Inverse Circular Functions * Identify the Inverse Functions Identify the Inverse Sine Function Identify the Inverse Cosine Function Identify the Inverse Tangent Function Identify the Inverse Function Values Trigonometric Equations Solve using Linear Methods Solve using Factoring Solve using Quadratic Methods Solve using Trigonometric Identities Identify Equations with Half-Angles Identify Equations with Multiple Angles Fourth Quarter at a Glance Throughout fourth quarter students will begin exploring the Law of Cosines, Vectors and Complex Numbers. Students will also apply skills learned in solving for the Area of a Triangle using the Heron’s Formula and convert from Polar to Rectangular Coordinate systems and vice versa. They shall also find the roots of complex numbers. By the end of Fourth Quarter Trigonometry students should be able to: Oblique Triangles and Law of Sines Solve Oblique Triangles Derive the Law of Sines Solve SSA and ASA Triangles Find the area of a triangle The Ambiguous Case of the Law of Sines Describe the Ambiguous Case Solve SSA Triangles (Case 2) Analyze data for possible number of triangles The Law of Cosines Derive the Law of Cosines Solve SAS and SSS Triangles (Cases 3 and 4) Heron’s Formula for the Area of a Triangle Vectors, Operations, and the Dot Product Define Basic Terminology Operate with Vectors Find the Dot Product and Angle between vectors Complex Numbers Understand basic concepts of Complex Numbers Find Complex solutions of Equations Perform Operations on Complex Numbers Trigonometric (Polar) Form of Complex Numbers Determine the Complex Plane and Vector Representation Define the Trigonometric (Polar) Form Convert between Rectangular and Trigonometric (Polar) Form De Moivre’s Theorem; Powers and Roots of Complex Numbers Solve for the roots of Complex Numbers