Download ELEMENTARY ALGEBRA

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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