Download MTH112ElementaryFunctions

Course No: MTH112
Credits:
4
Date: October 2010
Course Title:
Elementary Functions
Institution:
Rogue Community College
Type of Course:
Transfer
Length of Course:
A minimum of forty (40) lecture hours per one term.
Prerequisites:
MTH95 and RD30 or designated placement test score as shown on
current indicator chart.
Department Assignment:
Mathematics
Course Description: Elementary Functions covers basic and advanced trigonometry.
Course Outcomes, ILO (Institutional Learning Outcomes) Indicators and Assessment: On
successful completion of this course, the students will be able to:
Expected Outcomes:
1. Use mathematical problem
solving techniques involving
exponential, logarithmic and
trigonometric functions. These
techniques include data fitting
and the use of graphical,
symbolic, narrative and tabular
methods of analysis.
2. Use trigonometry in a variety
of applications in surveying,
engineering, navigation, and
others.
ILO Key Indicators:
Assessment Methods:
COM 2 - Express ideas
1. Criterion referenced tests and
clearly in oral, written and quizzes using pencil, paper and
visual work.
graphing calculators, daily
CT 3 - Locate, organize,
homework requiring analysis of
analyze, and interpret
data and information to arrive at
data.
a solution or conclusion, a
AK 2 - Integrate previous research project relating to
and new learning, along
topics studies in class.
with practical skills, to
solve problems.
Homework, tests, group work,
AK 4 - Use numeracy
class discussions, and
skills for interpretation,
instructor observation.
synthesis, and analysis of
data.
AL 3 - Internalize and
2. Criterion referenced tests and
assimilates information
quizzes using pencil, paper and
into new situations.
graphing calculators, daily
AK 1 - Demonstrate
homework requiring analysis of
ability to transfer learning data and information to arrive at
in familiar and unfamiliar a solution or conclusion.
contexts in order to
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Expected Outcomes:
3. Solve analytic geometry
problems involving
trigonometry.
4. Identify the need for data,
obtain it from existing sources,
and evaluate its relevance and
accuracy for problem solving.
5. Use inductive and deductive
reasoning to develop and verify
mathematical arguments.
6. Participate in problem solving
exercises and teach others as a
team member.
7. Select and analyze
information involving
ILO Key Indicators:
complete tasks.
AK 2 - Integrate previous
and new learning, along
with practical skills, to
solve problems.
AL 3 - Internalize and
assimilates information
into new situations.
AK 1 - Demonstrate
ability to transfer learning
in familiar and unfamiliar
contexts in order to
complete tasks.
AK 2 - Integrate previous
and new learning, along
with practical skills, to
solve problems.
CT 3 - Locate, organize,
analyze, and interpret
data.
AK 4 - Use numeracy
skills for interpretation,
synthesis, and analysis of
data.
Assessment Methods:
Homework, tests, group work,
class discussions, and
instructor observation.
CT 4 - Envision creative
approaches to issues and
problems.
AK 4 - Use numeracy
skills for interpretation,
synthesis, and analysis of
data.
5. Criterion referenced tests and
quizzes using pencil, paper and
graphing calculators, daily
homework requiring analysis of
data and information to arrive at
a solution or conclusion.
CT 4 - Envision creative
approaches to issues and
problems.
AK 2 - Integrate previous
and new learning, along
with practical skills, to
solve problems.
3. Criterion referenced tests and
quizzes using pencil, paper and
graphing calculators, daily
homework requiring analysis of
data and information to arrive at
a solution or conclusion.
Homework, tests, group work,
class discussions, and
instructor observation.
4. A research project relating to
topics studied in class.
Homework, tests, group work,
class discussions, and
instructor observation.
Homework, tests, group work,
class discussions, and
instructor observation.
6. Daily homework requiring
analysis of data and information
to arrive at a solution or
conclusion.
Homework, tests, group work,
class discussions, and
instructor observation.
COM 2 - Express ideas
7. Daily homework requiring
clearly in oral, written and analysis of data and information
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Expected Outcomes:
ILO Key Indicators:
trigonometric functions, and
visual work.
communicate the results to
others using oral, written,
graphic, pictorial, or multi-media
methods.
8. Approach practical problems
by choosing appropriate
mathematical techniques
outlined in the textbook, use
quantitative data to construct
logical explanations, and express
mathematical ideas and concepts
orally and in writing.
Assessment Methods:
to arrive at a solution or
conclusion, and a research
project relating to topics studied
in class.
Homework, tests, group work,
class discussions, and
instructor observation.
CT 3 - Locate, organize,
8. Criterion referenced tests and
analyze, and interpret
quizzes using pencil, paper and
data.
graphing calculators, daily
COM 2 - Express ideas
homework requiring analysis of
clearly in oral, written and data and information to arrive at
visual work.
a solution or conclusion, a
research project relating to
topics studied in class.
Homework, tests, group work,
class discussions, and
instructor observation.
9. Make use of the graphics
calculator as a tool to aid in the
problem solving process.
CT 3 - Locate, organize,
analyze, and interpret
data.
9. Criterion referenced tests and
quizzes using pencil, paper and
graphing calculators, daily
homework requiring analysis of
data and information to arrive at
a solution or conclusion.
Homework, tests, group work,
class discussions, and
instructor observation.
Typical Required and Recommended Text(s): Robert Blitzer, Pre-calculus, 4th edition, Prentice Hall
Publishing, 2010.
Typical Required and Recommended Equipment and Materials: Graphing calculator (TI83, TI-83 Plus, or TI-84 Plus), graph paper, pencil, paper, and notebook.
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TYPICAL COURSE OUTLINE:
Trigonometric Functions (approx. 33% of course)
Angles and Their Measure
Use degree measure
Draw angles in standard position
Find coterminal angles
Complementary and supplementary angles
Use radian measure
Convert between degree and radian measures
Arc length
Linear and angular motion
Trigonometric Functions: The Unit Circle
Unit circle definitions of the trigonometric function
Use the unit circle to find values of the trigonometric functions
Domain and range of the sine and cosine functions
Find exact values of trigonometric function of common angles
Recognize and use fundamental identities
Use periodic properties
Evaluate trigonometric functions with a calculator
Right Triangle Trigonometry
Use right triangles to evaluate trigonometric functions
Find trigonometric function values for common angles
Use equal cofunctions of complements
Applications
Trigonometric Functions of Any Angle
Definitions of trigonometric functions of any angle
The signs of trigonometric functions
Reference angles and how they are used
Graphs of the Sine and Cosine Functions
The graph of sin(x)
The transformations of the graph of sin(x)
The graph of cos(x)
The transformations of the graph of cos(x)
Model periodic behavior
Sinusoidal curve fitting using data points
Graphs of Other Trigonometric Functions
The graph of tan(x) and its transformations
The graph of cot(x) and its transformations
The graph of csc(x) and sec(x) and their transformations
Inverse Trigonometric Functions
Inverse sine function
Inverse cosine function
Inverse tangent function
Use calculator to evaluate inverse trigonometric functions
Find exact values of composite functions with inverse trigonometric functions
Applications of Trigonometric Functions
Solving right triangles
Solving problems involving bearings
Modeling simple harmonic motion
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Analytic Trigonometry (approx. 33% of course)
Verifying Trigonometric Identities
Use the fundamental trigonometric identities to verify other identities
Sum and Difference Identities
Use the formula for the cosine of the difference of two angles
Use the sum and difference formulas for cosines and sines
Use the sum and difference formulas for tangents
Double-Angle and Half-Angle Identities
Use the double angle formulas
Use the power-reduction formulas
Use the half angle formulas
Product-to-Sum and Sum-to-Product Formulas (OPTIONAL)
Trigonometric Equation
Find all solutions of a trigonometric equation
Solve equations with multiple angles
Solve quadratic trigonometric equations
Use factoring
Use identities to solve trigonometric equations
Additional Topics in Trigonometry (approx. 33% of course)
The Law of Sines
Use the Law of Sines to solve oblique triangles
Use the Law of Sines to solve the ambiguous case
Find the area of an oblique triangle using the sine function
Applications using the Law of Sines
The Law of Cosines
Use the Law of Cosines to solve oblique triangles
Applications using the Law of Cosines
Heron’s formula
Polar Coordinates
Plot points in the polar coordinate system
Find multiple sets of polar coordinates for a given point
Covert from polar to rectangular coordinates and vice-versa
Convert an equation from rectangular to polar form and vice-versa
Graphs of Polar Equations
Circles, lines, Limacons, Rose curves, and Lemniscates
Complex Numbers in Polar Form; DeMoivre’s Theorem (OPTIONAL)
Vectors (in two dimensions)
Equality of vectors
Scalar multiplication, vector addition and subtraction
Vectors in the rectangular coordinate system
Component form of vectors
Applied vector problems
The Dot Product
Find the dot product of two vectors
Find the angle between two vectors
Orthogonality
Projections of a vector onto another
Applications
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