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: / ILO Key Indicators: / Assessment Methods: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. / COM 2 - Express ideas clearly in oral, written and visual work.
CT 3 - Locate, organize, analyze, and interpret data.
AK 2 - Integrate previous and new learning, along with practical skills, to solve problems.
AK 4 - Use numeracy skills for interpretation, synthesis, and analysis of data. / 1. 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, a research project relating to topics studies in class.
Homework, tests, group work, class discussions, and instructor observation.
2. Use trigonometry in a variety of applications in surveying, engineering, navigation, and others. / 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. / 2. 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.
3. Solve analytic geometry problems involving trigonometry. / 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. / 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. Identify the need for data, obtain it from existing sources, and evaluate its relevance and accuracy for problem solving. / CT 3 - Locate, organize, analyze, and interpret data.
AK 4 - Use numeracy skills for interpretation, synthesis, and analysis of data. / 4. A research project relating to topics studied in class.
Homework, tests, group work, class discussions, and instructor observation.
5. Use inductive and deductive reasoning to develop and verify mathematical arguments. / 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.
Homework, tests, group work, class discussions, and instructor observation.
6. Participate in problem solving exercises and teach others as a team member. / CT 4 - Envision creative approaches to issues and problems.
AK 2 - Integrate previous and new learning, along with practical skills, to solve problems. / 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.
7. Select and analyze information involving trigonometric functions, and communicate the results to others using oral, written, graphic, pictorial, or multimedia methods. / COM 2 - Express ideas clearly in oral, written and visual work. / 7. Daily homework requiring analysis of data and information 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.
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. / CT 3 - Locate, organize, analyze, and interpret data.
COM 2 - Express ideas clearly in oral, written and visual work. / 8. 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, 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.
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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 (TI-83, TI-83 Plus, or TI-84 Plus), graph paper, pencil, paper, and notebook.
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
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
DoubleAngle and HalfAngle 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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