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LAKELAND COMMUNITY COLLEGE -
COURSE OUTLINE FORM
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ORIGINATION
DATE: 08/02/99 APPROVAL DATE: /
/
LAST
MODIFICATION DATE: 09/05/00
EFFECTIVE TERM/YEAR: FALL 2000
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PRINTED: 02/20/03
COURSE
NUMBER: MATH1700
COURSE
TITLE: Trigonometry
LECTURE LAB
CLINICAL TOTAL OBR MIN OBR MAX
CREDITS: 3.00 0.00 0.00 3.00 3.00 3.00
CONTACT
HOURS: 3.00 0.00 0.00 3.00
PREREQUISITES:
MATH1650 OR PERMISSION OF INSTRUCTOR
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PROGRAMS
& CERTIFICATES FOR WHICH THIS COURSE IS REQUIRED:
3701 - Chemical Technician Certificate
PROGRAMS
& CERTIFICATES FOR WHICH THIS COURSE IS AN ELECTIVE:
9000 - Associate of Arts-Transfer
9099 - TRANSFER MODULE
9100 - Associate of Science-Transfer
COURSE
ACCEPTED AS TRANSFER CREDIT BY:
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RECOMMENDED
CLASS SIZE: 30 RATIONALE: DEPARTMENT STANDARD
FREQUENCY
OF OFFERING: 3 X YEAR
TERMS
NORMALLY OFFERED: FALL SPRING
SUMMER
LAB
FEE: NONE
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RATIONALE
FOR COURSE:
This course serves as a prerequisite for the
Analytical Geometry Calculus
sequence, as well as a foundation course for
Engineering and Science majors.
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COURSE
DESCRIPTION:
This
course includes the study of trigonometric functions and inverse
trigonometric
functions and their graphs; solutions of right and oblique
triangles
and their applications; solutions of trigonometric equations and
inequalities;
the use of identities, vectors, and complex numbers; and
solutions
of polar equations and parametric equations.
Students must
supply
a graphing calculator.
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GENERAL
COURSE GOALS:
1. Further
develop students' ability to use the language of mathematics
correctly
in speaking and writing.
2. Introduce
and develop, in a mathematically rigorous manner, the
concepts
and applications of the trigonometric functions.
3. Further
develop the use of technology (graphing calculator and
computer)
as a tool for solving problems.
4. Further
develop students' abilities to solve real-life problems
utilizing
the trigonometric functions and analyze and solve these
problems
analytically and graphically.
5. Engage
students in the exploration of the central ideas of
trigonometry
through laboratory experiments, individually and/or in
groups.
6. Further
strengthen students' ability to critically apply
mathematical
thinking to solve problems and to determine
reasonableness
of results.
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COURSE
OBJECTIVES:
Upon completion of the course, the student
should be able to:
1. Define
the six trigonometric functions as circular functions.
2. Define
the six trigonometric functions of angles given a point on the
terminal
side of an angle in standard position.
3. Define
the six trigonometric functions for an acute angle within a
right
triangle.
4. Evaluate
the trigonometric functions of angles in radian and degree
measure
exactly using the unit circle and approximately using a
calculator.
5. Graph
the six trigonometric functions and determine horizontal shifts,
vertical
shifts, period and amplitude changes.
6. Solve
right triangles; apply right triangles to real-world problems.
7. Solve
oblique triangles using the Law of Sines and Law of Cosines;
apply
to real-world problems.
8. Apply
the fundamental trigonometric identities.
9. Graphically
and analytically verify identities.
10. Solve
and apply trigonometric equations graphically and analytically.
11. Define
the inverse trigonometric functions.
12. Graph
the inverse trigonometric functions.
13. Convert
from Cartesian coordinates to polar coordinates and
vice-versa.
14. Graph
in polar coordinates.
15. Analyze
the path of objects via parametric equations and their graphs.
16. Analyze
basic forces via vectors.
17. Represent
complex numbers in trigonometric form.
18. Analyze
power and roots of complex numbers.
19. Apply
De Moivre's Theorem.
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COURSE
OUTLINE:
I. Algebra
Topics
A. Functions and Graphs
1. Function notation
2. Domain and range
3. Inverses
4. Intervals of increasing and decreasing
behavior
5. Concavity
II. Angles
A. Radian and Degree measurement
B. Positive, Negative and Coterminal
C. Standard Position
III. Circular
Functions
A. Unit circle and definition of 6 trigonometric
functions
B. Sine and Cosine Functions
1. Function values for cos x and sin x via unit
circle
C. Tangent Function
D. Cosecant, Secant and Cotagent Functions
IV. Graphs
A. Graphs of all 6 trigonometric functions
B. Periodic Functions
1. Model periodic behavior with appropriate
function
C. Inverse Trigonometric Functions
1. Definitions
2. Notation
3. Graphs
V. Triangles
A. Right Triangles
1. Definition of 6 trigonometric functions
2. Solution
3.
Applications
B. Oblique Triangles
1. Law of Sines
a.
Applications
2. Law of Cosines
a. Applications
C. Similar
Triangles
1. Definition of 6 trigonometric functions via
any point
on
terminal side of angle in standard position.
2. Applications
VI. Identities
and Equations
A. Fundamental Identities
1. Reciprocal identities
2. Quotient identities
3.
Pythagorean identities
B. Sum and Difference identities
1. Sine, cosine and tangent
C. Double Angle identities
1. Sine, cosine and tangent
D. Additional identities
1. Half-angle
E. Verification
1. Graphical and analytical
F. Conditional equations
1. Solving via graphical and analytical methods
VII. Vectors
A. Definition
B. Algebra of vectors
1. Addition
2.
Subtraction
3. Scalar multiplication
4. Dot product
C. Applications
1. Forces
2.
Angles
VIII. Parametric
Equations, polar coordinates and Polar equations
A. Definition
B. Analysis via rule of three
1. Numerical
2. Graphical
3. Analytical
C. Applications
1. Paths of objects
2. Angle approximations
D. Polar Coordinates
1. Convert from Cartesian coordinates to polar
coordinates
and vice-versa
2.
Graph in polar coordinates
a. Lines
b.
Circles
c. Limacons
d.
Lemniscates
e. Roses
f.
Cardioids
3. Symmetry of graphs
E. Polar/Trigonometric form of Complex Numbers
1. Powers and roots of complex numbers
a. De Moivre's Theorem
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INSTRUCTIONAL
PROCEDURES THAT MAY BE UTILIZED:
Lecture/discussion, computer/graphing
calculator based activities, group
and/or individual activities, research
projects utilizing real data gathered
from the Internet or other sources.
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SUGGESTED
GRADING PROCEDURES:
It is recommended that instructors have at
least five evaluative items on
which to determine student's final
grade. In general, tests are given
covering the lecture and homework
assignments.
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SUGGESTED
COURSE EVALUATION PROCEDURE:
Student course evaluations.
Student success rate in subsequent Math
courses.
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[ End
of Course Outline for 'MATH1700' ]
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COURSE OUTLINE -- GENERAL
EDUCATION OUTCOMES
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COURSE ID: MATH1700 PRINTED:
02/20/03
TITLE: Trigonometry
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| General Education | Methods of |
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*** KNOWLEDGE *** |
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1. Arts and Literature | | | | | | | | | |
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2. Complexities of Human Behavior | | | | | | | | | |
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3. Complexities of Social Institutions | | | | | | | | | |
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4. Math and Science |1| | | | | | | | |
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5. Past and Present Cultures | | | | | | | | | |
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6. Technology |1| | | | | | | | |
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*** CRITICAL THINKING *** |
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| 7.
Identify Personal Assumptions | | | | | | | | | |
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8. Identify Ethical Dimensions | | | | | | | | | |
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9. Examine Issues by Suspending/Challenging Assumpt | | | | | | | | | |
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| 10. Evaluate Issues from Various Perspectives | | | | | | | | | |
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| 11. Collect, Analyze, Interpret
Information | | | | | | | | | |
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| 12. Support Hypotheses | | | | | | | |
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| 13. Synthesize Information |1| | | | | | | | |
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| 14. Draw Conclusions |1| | | | | |
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*** COMMUNICATION SKILLS *** |
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| 15. Speak Clearly and Effectively | | | | | | | | | |
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| 16. Read with Comprehension | | | | | | | | | |
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| 17. Write Clearly & Effectively in
Standard English | | | | | | | | | |
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| 18. Work Effectively in Groups | | | | | | | | | |
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19. Listen Actively and with Understanding | | | | | | | | | |
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| 20. Practice Effective Interpersonal
Skills | | | | | | | | | |
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| 21. Interpret/Use Graphic
Communication |1| | | | | |
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| 22. Use Technology-Based Communication |1| | | | | | | | |
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| Methods of Assessment codes: |
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| 1. Test/Examination | 4. Collaborative Writing | 7.
Portfolio |
| 2. Homework/Written | 5. Oral Presentation | 8. Demonstration of |
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Assignment | | Skills |
| 3. Research Paper | 6. Lab Project | 9. Other (specify)
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