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MTH 122 Sec 208
Plane Trigonometry
Specific Course Information
Spring 2009
Instructor: Dr. Clayton Brooks ([email protected])
SH 742D
696-6702
Office Hours: T & Th 12:30 – 2:00, 8:00 – 9:00 pm (or by appointment)
Text: College Trigonometry 6/e by Aufmann, Barker, & Nation
Calculator: Given that you are or have taken College Algebra, you must have a TI-83 (or higher)
graphing calculator, which will be used frequently. Tests will contain problems requiring
a calculator and problems in which a calculator will not be allowed. On test day, you
must have your own calculator – no sharing allowed.
Attendance: will be noted. Excessive absences will not be counted against you, but they may
indicate your lack of a desire to succeed and relieve me of my obligation to assist you.
You are responsible for any assignments or important notices that you may have missed.
Missing exams is not acceptable. You will not be allowed to make up any exam.
You will get a zero, but everyone is allowed to drop their lowest test score. An exception
to this policy is if you have an official university obligation. However, you must inform
me well in advance.
Homework: for the most part, will not be handed in (I will tell you in advance if it is).
Mathematics cannot be learned passively, and again, your failure to do assignments
indicates your lack of a desire to succeed and relieves me of any obligation to assist you.
The late policy is 1% reduction in credit per hour.
Cellular phones: In spite of a society that says otherwise, or unless you are an emergency
worker that is “on call”, you do not need a cellular phone turned on at all times. It only
serves to distract you and the rest of the class. Turning it to vibrate-mode is no better.
We can still hear it. Save your battery. Turn it off. Retrieve messages after class.
Tutoring: is available, free of charge, from the Math Department in SH 526 each day.
Also, the University provides personal and drop-in tutoring through the Tutoring Center
(www.marshall.edu/uc/MATH.pdf). And, I’m available after hours, by appointment.
Grading Policy: Tests (3 – lowest score dropped) 200
Final (cumulative)
+200
400
Important Dates:
Last day to drop
Final exam
90% = A
80% = B
70% = C
60% = D
March 20
Tuesday, May 5 (7:00 – 9:00)
Spring 2009 Tentative Schedule
MTH 122 (Section 208)
Week
Sections Covered
Topics
1
Jan 13, 15
2
Jan 20, 22
3
Jan 27, 29
4
Feb 3, 5
5
Feb 10, 12
6
Feb 17, 19
7
Feb 24, 26
8
Mar 3, 5
9
Mar 10, 12
10
Mar 17, 19
Chapter 1, 2.1
Algebra review. Angles. Degree & radian measure.
Arcs. Arc length. Angular speed.
Trigonometric functions. Special angle trig values.
Right triangle applications. Trig values for any angle.
Trig functions of real numbers & their properties.
Graphs of sine and cosine functions.
Graphs of tangent and secant functions.
Graphing techniques.
Test 1 on February 12.
2.2, 2.3
2.4, 2.5
2.6, 2.7
Test
3.1, 3.2
3.3
3.5
3.6
Test
Fundamental trig identities. Verifying trig identities.
Sum, difference & cofunction identities.
Double angle, power reducing
& half angle identities.
Inverse trig functions, compositions, & their graphs.
Solving trigonometric equations,
algebraically & graphically.
Test 2 on March 19.
(Spring Break)
Mar 24, 26
11
Mar 31, Apr 2
12
Apr 7, 9
13
Apr 14, 16
14
Apr 21, 23
15
Apr 28, 30
Finals
May 5
4.1, 4.2
4.3, 5.1
5.2, 5.3
Test
6.5, Review
Final Exam
The secret to ridiculous wealth. Law of sines.
Law of cosines. Area of triangles.
Vectors. Unit vectors. Dot product. Projections.
Introduction to complex numbers.
Trig form of complex numbers & products.
DeMoivre’s Theorem & finding roots.
Test 3 on April 23.
Introduction to polar coordinates.
Review for final exam.
Tuesday 7:00 – 9:00
GENERAL SYLLABUS FOR MTH 122
TRIGONOMETRY
CATALOG DESCRIPTION
Trigonometry: 3 hrs. A study of the trigonometric functions, graphs of the trigonometric
functions, identities, equations, inverse trigonometric functions, vectors, complex numbers, and
applications. (PR: One-half year of high school geometry. PR or CR: MTH 127 or MTH 130 or
MTH 130H or at least 21 on Mathematics ACT or at least 530 on Mathematics SAT.
Course Objectives: To present a comprehensive development of trigonometry and
some of the applications of trigonometry. To help prepare students for courses in
calculus and analytic geometry. To help prepare students for study in areas such as
physics, engineering, biology, chemistry, pharmacy, geology, and medicine.
Course Outline: Note that there are a large number of optional topics available so that
the instructor has some leeway in designing the course according to his or her interests.
I.
RIGHT TRIANGLE RATIOS
a. Angles, Degrees, and Arcs
b. Similar Triangles
c. Trigonometric Ratios and Right Triangles
d. Right Triangle Applications
II.
TRIGONOMETRIC FUNCTIONS
a. Degrees and Radians
b. Linear and Angular Velocity (OPTIONAL)
c. Trigonometric Functions
d. Additional Applications (OPTIONAL)
e. Exact Value for Special Angles and Real Numbers
f. Circular Functions
III.
GRAPHING TRIGONOMETRIC FUNCTIONS
a. Basic Graphs
b. Graphing y=k+A sin Bx and y=k+A cos Bx
c. Graphing y=k+A sin (Bx + C) and y=k+A cos (Bx + C)
d. Additional Applications (OPTIONAL)
e. Graphing Combined Forms (OPTIONAL)
f. Tangent, Cotangent, Secant, and Cosecant Functions Revisited
IDENTITIES
a. Fundamental Identities and their Use
b. Verifying Trigonometric Identities
c. Sum, Difference, and Cofunction Identities
IV.
d. Double-Angle and Half-Angle Identities
e. Product-Sum and Sum-Product Identities (OPTIONAL)
V.
INVERSE TRIGONOMETRIC FUNCTIONS;
TRIGONOMETRIC EQUATIONS AND INEQUALTIES
a. Inverse Sine, Cosine, and Tangent Functions
b. Inverse Cotangent, Secant, and Cosecant Functions (OPTIONAL)
c. Trigonometric Equations: An Algebraic Approach
d. Trigonometric Equations and Inequalities: A Graphing Utility
Approach (OPTIONAL)
VI. ADDITONAL TOPICS: TRIANGLES AND VECTORS
a. Law of Sines
b. Law of Cosines
c. Areas of Triangles (OPTIONAL)
d. Vectors: Geometrically Defined
e. Vectors: Algebraically Defined
f. The Dot Product
VII. POLAR COORDINATES; COMPLEX NUMBERS
a. Polar and Rectangular Coordinates
b. Sketching Polar Equations (OPTIONAL)
c. Complex Numbers in Rectangular Form and Polar Form
d. De Moivres’s Theorem and the nth Root Theorem
LEARNER OUTCOMES:
1 RIGHT TRIANGLE RATIOS
1.1 The student will determine the measure of angles using degree
measure and will recognize the proportion relating central angles
and arcs.
1.2 The student will recognize similar triangles, learn Euclid’s
Theorem, and will apply these ideas to a variety of applications.
2
1.3 The student will define trigonometric functions for acute angles
in terms of trigonometric ratios, explore complementary angles
and cofunctions, and compute values using a calculator.
1.4 The student will solve word problems that use right triangles.
TRIGONOMETRIC FUNCTIONS
2.1 The student will determine the measure of angles using radian
measure and will convert between radian and degree measure.
2.2 The student will explore angular and linear velocity for rotation
circular objects.
2.3 The student will define trigonometric functions for general angle
domains and also for real number domains. In additional the
student will investigate an application involving wind generators.
2.4 The student will explore applications of real-world trigonometry;
possible topics include refraction, and also the modeling of light
waves, rainbows, sonic booms, particle energy, and perception in
psychology by trigonometric functions.
2.5 The student will learn the exact values for special angles and for
real numbers without use of a calculator.
2.6 The student will define the circular functions and explore some
of the fundamental identities as well as periodicity.
3
GRAPHING TRIGONOMETRIC FUNCTIONS
3.1 The student will draw the basic graphs of the six trigonometric
functions by use of pencil and paper and by use of a graphing
calculator.
3.2 The student will draw the graphs of y=k+A sin Bx and
y=k+A cos Bx by hand and by use of a graphing calculator,
with special emphasis on the properties of the functions such as
amplitude, periodicity, and shifting techniques.
3.3 The student will sketch the graphs of y=k+A sin (Bx + C) and
y=k+A cos (Bx + C) by hand and by use of a graphing calculator,
with emphasis on phase-shift.
3.4 The student will explore one or more additional modeling
applications of graphing; topics include electric current,
electromagnetic waves, water waves, simple and damped harmonic
motion, and resonance.
3.5 The student will investigate the graphs of the sum of two of more
trigonometric graphs as well as applications, such as sound waves
and Fourier Series.
3.6 The student will focus on sketching the graphs of the remaining
four trigonometric functions, focusing on shifting techniques, and
periodicity.
4
IDENTITIES
4.1 The student will learn and use the fundamental trigonometric
identities.
4.2 The student will verify general trigonometric identities
algebraically using the fundamental identities.
4.3 The student will use the sum, difference, and cofunction identities
for the sine, cosine, and tangent functions.
4.4 The student will use the double-angle, and half-angle identities for
the sine and cosine functions.
4.5 The student will solve problems that require changing products of
sine and/or cosine functions to sums or sums to products.
In addition, the students will explore the application of these
identities to music.
5 INVERSE TRIGONOMETRIC FUNCTIONS;TRIGONOMETRIC
EQUATIONS AND INEQUALITIES
5.1 The student will define the inverse sine, cosine, and tangent
functions and sketch their graphs. Moreover, the student will
explore applications to space science and precalculus.
5.2 The student will define the inverse cotangent, secant, and
cosecant functions and will sketch graphs for these functions.
5.3 The student will algebraically solve trigonometric equations,
and will examine applications to photography and astronomy.
5.4 The student will solve trigonometric equations and inequalities
using a graphing calculator, and will explore applications to
geometry and architecture.
6
ADDITIONAL TOPICS: TRIANGLES AND VECTORS
6.1 The student will know the Law of Sines and will use it to solve
a variety of applied word problems.
6.2 The student will know the Law of Cosines and will use it to solve
word problems, including navigation and precalculus problems.
6.3 The student will calculate areas of triangles using various
methods involving Heron’s formula.
6.4 The student will focus on geometrically defined planar vectors,
including the calculation of the sum, the resultant, and the
magnitude of such vectors. Applications to physics are
emphasized.
6.5 The student will focus on algebraically defined planar vectors,
making the connection to geometry and including the
computation of scalar multiplication, unit vectors, and
the general algebraic properties of vectors.
6.6 The student will define the dot product of two vectors and apply
this to the calculation of the angle between two planar vectors,
including whether two vectors are orthogonal, parallel, or
neither. Also the student will determine the orthogonal
projection of one vector onto another.
7
POLAR COORDINATES; COMPLEX NUMBERS
7.1 The student will be introduced to the polar coordinate
system and learn how to convert between polar coordinates and
rectangular coordinates.
7.2 The student will sketch the graphs of basic polar equations by
hand and by calculator.
7.3 The student will learn to convert a complex number to
trigonometric form and reverse-wise. In addition the student will
multiply and divide complex numbers using the trigonometric
form of the numbers.
7.4 The student will calculate powers of complex numbers using
DeMoivre’s theorem, will calculate roots of complex number
using the nth-Root Theorem, and will use the roots of complex
numbers to solve equations.
METHODS OF EVALUATION: Learner outcomes will be evaluated by use of a
combination of in-class exams, a comprehensive final exam, quizzes, and group activities
subject to instructor interest. The text provides many excellent group activities for use in
the course.