1
MATH 1720
PreCalculus II
MWF . . . . . 11:15 am – 12:10 pm . . . . . Warf 104 . . . . . FALL / 2009
https://elearn.volstate.edu
Mr. Ondis Bible
Associate Professor of Mathematics
http://www2.volstate.edu/OBible
DESCRIPTION:
Designed as a course for students who plan to major in mathematics and/or
science and are not prepared to take calculus. Topics include the trigonometric
functions of the acute and general angle, applications of right triangles, identities,
related angles and the reduction formula, radian measure, graphs and graphical
methods of the trigonometric functions, applications, inverse trigonometric
functions. PREREQUISITES: MATH 1710 with a grade of C or better or MATH
1130 with a grade of A and an acceptable placement score. (Same as RODP
MATH 1720)
TEXTBOOK:
MATH 1720 Bundle: Algebra and Trigonometry with Analytic Geometry, (Custom
12th Edition) Swokowski and Cole, WebAssign Access Code, Presentations CD.
Optional Supplementary Text: Student's Solutions Manual, Cole. Copies of this
book and supplement are available for purchase in the VSCC Bookstore or Online.
INSTRUCTOR:
Ondis Bible, Associate Professor of Mathematics, Office Warf-100H, Phone (615)
230-3386 or ext. 3386 at (615) 741-3215 or (615) 452-8600 or (888) 335-8722,
FAX (615) 230-3292, Email ondis.bible@volstate.edu Address: VSCC, 1480
Nashville Pike, Gallatin, TN 37066-3188
OFFICE HOURS:
Posted beside office door (Warf 100H) and on the Internet. Go to
http://www2.volstate.edu/OBible and click on [Office Hours].
GENERAL
EDUCATION GOAL
The general education goal of this course is to expose students to systems of mathematical logic.
GENERAL
EDUCATION
OUTCOMES
As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the
basic concepts and principles of trigonometry and an understanding of mathematical logic necessary to apply these
concepts and principles to problem solving. Acceptable mastery of the course contents will indicate a trigonometry
background necessary to pursue further course work in mathematics and other areas in which Pre-Calculus II is a
prerequisite.
OTHER GOALS
This course also serves to develop effective communication skills, particularly in reading and understanding directions.
OUTCOME
STATEMENTS
Upon completion of this course the student will have demonstrated an acceptable ability to:
1.
2.
3.
4.
Define a trigonometric angle and its component parts.
Define the standard position of an angle.
Know the definitions of the six trigonometric functions.
Draw an angle in standard position, given one function of that angle, and find the other trigonometric functions.
5. Find the values of the six trigonometric functions for multiples of
6.
7.
8.
9.
10.
11.
12.
 / 6 and  / 4.
Know the sign of each trigonometric function in each quadrant.
Define cofunctions.
Know the cofunction identities.
Determine the correct number of significant digits when rounding sides of a triangle.
Given an angle, find one of its functions.
Given a function of an angle, find the angle.
Find the values of trigonometric functions by using a calculator.
2
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Solve simple problems involving right triangles.
Distinguish between angles of elevation and depression.
Solve problems using angles of elevation and depression.
Determine the bearing of a line.
Memorize the basic trigonometric identities.
Prove other identities by using the basic identities.
Find values of some trigonometric functions, from others which are known, by using basic identities.
Distinguish between identities and conditional equations.
Define related angles.
Reduce angles to functions of an acute angle.
23. Memorize and use the trigonometric functions of
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
( ).
Solve problems using the cofunction identities.
Convert radians to degrees and degrees to radians.
Compute arc length on a circle.
Given an angular speed and a radius, find linear speed.
Given angular speed, radius, and time, find total distance traveled.
Given speed and radius, find angular speed.
Given speed, radius, and time, find total amount of rotation.
Sketch the graphs of the six trigonometric functions.
Know the meaning of period, cycle, increasing and decreasing functions.
Give the domain, range, and period of the six trigonometric functions.
Know the meaning of an identity, equivalent equation, and conditional equation.
Find solution sets of trigonometric equations.
(0, 2 ).
(0, 360).
36. Solve simple trigonometric equations not requiring the use of tables or a calculator, finding all solutions, or all solutions in
37. Solve simple trigonometric equations requiring the use of tables or a calculator, finding all solutions, or all solutions in
38.
39.
40.
41.
42.
43.
44.
Know the identities involving the sine, cosine, and tangent of the sum or difference of two real numbers.
Compute using the trigonometric identities.
Prove other identities by using these identities.
State the double-angle and half-angle formulas.
Use the double-angle identities to find function values of twice an angle when one function value is known for that angle.
Use the half-angle identities to find the function values of half an angle when one function value is known for that angle.
Simplify certain trigonometric expressions using the half-angle and double-angle formulas.
45. Solve equations containing trigonometric functions of
2 ,  / 2, 3 , etc.
46. Solve equations containing trigonometric functions of different quantities.
47. Solve equations of the form, a sin dx  b cos dx  c.
48. Solve trigonometric equations by factoring or using the quadratic formula.
49. Know the meaning of the terms, amplitude, period, and phase shift.
y  a sin (bx  c) and y  a cos (bx  c).
Sketch the graphs of y  a sin (bx  c), y  a cos (bx  c), and y  a tan bx.
Sketch graphs of y  a  b sin( cx  d ) and y  a  b cos( cx  d ) for various values of the constants a, b, c, and d.
50. Give the amplitude, period, and phase shift of
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
For functions like these, determine the amplitude, period, and phase shift.
Know the Law of Sines and the Law of Cosines.
Use the Law of Sines to find a side of a triangle.
Use the Law of Sines to solve any triangle, given a side and two angles.
Use the Law of Sines to solve triangles, given two sides and an angle opposite one of them, finding two solutions when they exist, and
recognizing when a solution does not exist.
Solve applied problems requiring the use of the Law of Sines.
Use the Law of Cosines to find a side of a triangle.
Use the Law of Cosines to find an angle of a triangle.
Use the Law of Cosines, with the Law of Sines, to solve any triangle, given two sides and the included angle.
Use the Law of Cosines to solve any triangle, given three sides.
Solve applied problems requiring use of the Law of Cosines.
Find all parts of a triangle by using the Law of Sines, Law of Cosines, or both.
Find the area of a triangle under the following conditions:
a. If 2 sides and the included angle are given.
b. If 3 angles and 1 side are given.
c. If 3 sides are given.
Know the definition of an inverse relation and inverse function.
Be familiar with the inverse functions corresponding to y = sin x, y = cos x, & y = tan x.
Given a number a, find all values of arcsin a, arccos a, and arctan a, in degrees---also in radians if a is a number for which use of a table
or calculator is not required.
Immediately simplify expressions such as sin arcsin x, to x.
Simplify expressions like arcsin sin x. If x is in the domain of the inverse function, immediately simplify to x.
Simplify expressions involving combinations such as sin arccos (1/2) without using tables or a calculator.
Simplify expressions such as sin arctan (a/b) by drawing a triangle and reading off appropriate ratios.
Use trigonometric identities to simplify expressions involving combinations of functions when appropriate.
Define Principal Values for the inverses of the trigonometric functions.
Find Principal Values of the inverses of the trigonometric functions.
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TOPICAL OUTLINE
The Trigonometric Functions
Trigonometry
Directed Segments
Trigonometric Angles
Standard Position of an Angle
Trigonometric Functions of an Angle
Trigonometric Functions of an Acute Angle
Cofunctions
Variation of the Functions of an Acute Angle
The Trigonometric Functions of
30, 45, 60
Approximations and Significant Figures
A Table of Trigonometric Functions
The Solution of Right Triangles
Angles of Elevation and Depression
Bearing of a Line
Vectors
Trigonometric Identities
The Fundamental Relations
Algebraic Operations with the Trigonometric Functions
Identities and Conditional Equations
Trigonometric Identities
Related Angles
Reduction to Functions of an Acute Angle
Trigonometric Functions of
Radian Measure
The Radian
Radians and Degrees
Length of a Circular Arc
The Circular Functions
Linear and Angular Velocity
(  )
Graphs of the Trigonometric Functions
Periodic Functions
Variations of the Sine and Cosine
Variation of the Tangent
Graphs of the Trigonometric Functions
Trigonometric Equations
Solving a Trigonometric Equation
Graphical Methods
The Graph of y = a sin bx
The Graph of y = a sin (bx + c)
The Graph of y = sinn x
Sketching Curves by Composition of y-Coordinates
The Graph of y = a sin x + b cos x
Functions of Two Angles
Functions of the Sum of Two Angles
sin (A + B) and cos (A + B)
tan (A + B)
sin (A - B), cos (A - B), and tan (A - B)
Double-Angle Formulas
Half-Angle Formulas
Inverse Trigonometric Functions
Inverse Trigonometric Relations
Inverse Trigonometric Functions
Operations Involving Inverse Trigonometric Functions
Oblique Triangles
The Law of Sines
Applications of the Law of Sines: SAA
The Law of Cosines
Applications of the Law of Cosines: SAS and SSS
ASSESSMENT: The degree to which the general education goal of this course is achieved will be determined by the cumulative assessment of the course
outcomes. Further assessment of the achievement of this goal and of the instructor will be provided by means of a student questionnaire.
The degree to which skills in effective communication have been developed can only be assessed to a limited extent. However, poor skills in reading and
understanding directions will result in lower grades on examinations.
Outcome statements will be assessed by homework assignments, short quizzes, major tests, and a comprehensive final examination.
ADA STATEMENT: For students with disabilities:
It is the student’s responsibility to self-identify with the Office of Disability Services to receive accommodations and services in accordance with The
Americans with Disabilities Act (ADA). Only those students with appropriate documentation and who are registered with the Office of Disability Services will
receive accommodations. For further information, contact the Office of Disability Services at (615) 230-3472, TDD (615)-230-3488, or visit the office which
is located in Room 108, Wood Campus Center.
EQUAL OPPORTUNITY STATEMENT: Volunteer State Community College is an equal opportunity Affirmative Action Educational Institution. No person
shall be excluded from participation in, be denied the benefit of, or be subjected to discrimination under any program or activity of the College because of
race, color, national origin, age, or handicap. The college also complies with the Age Discrimination in Employment Act of 1967, as amended and with the
Vietnam Era Veterans' Readjustment Act of 1974. The commitment to equal opportunity applies to all aspects of recruitment, employment and education of
individuals at all levels throughout the College.
4
COURSE POLICIES AND PROCEDURES
WEB-ENHANCED FORMAT: Some components of the course will be administered online. You may
use any computer that has Internet access --- at your home, workplace, or one of the VSCC computer
labs. Go to https://elearn.volstate.edu to enter the course. Your Username is the same as your VSCC
Student Email. Your Password is the same as your Pride Online password.
ATTENDANCE: Prompt and regular attendance is expected. Attendance will be recorded for each
class meeting. Absences in excess of five could result in the student being administratively withdrawn
from the course by the instructor. (See the VSCC Catalog.) Students on financial aid are reminded that
not attending class may result in the requirement that grant money be repaid.
TARDINESS is defined as entering the room after the official starting time for the class. Two instances
of tardiness will count as one absence. It is the responsibility of a student who is tardy, at the end of the
class, to ask the instructor to modify the attendance record. Tardiness is considered an avoidable class
disruption; persistent tardiness will not be tolerated. Any student who already has two instances of
tardiness must get to class on time --- or face the possibility that your grade will be adversely
affected (unless you are late due to an unexpected emergency that can be documented).
LEAVING CLASS EARLY (before dismissal by the instructor) is permitted in emergency situations. In
non-emergency cases, such as a doctor’s appointment, the student should notify the instructor at the
beginning of class that he/she will be leaving early and should sit close to the door in order to minimize
disruption to the class.
The INCLEMENT WEATHER POLICY for this class is as follows: If VSCC is officially open, this class
will meet as scheduled, all assignments will be due, and any scheduled tests or quizzes will be given. If
VSCC is officially closed, all assignments or tests scheduled for that day are automatically rescheduled
for the next regular class meeting.
If you miss class, or need additional instruction, view the relevant online PowerPoint Presentation
before attempting the homework. If you have technical problems with your computer or the online
components of this course, get the necessary assistance immediately. Call the VSCC Help Desk, ext.
3367. To log into the online component of the course, go to https://elearn.volstate.edu and log in to
D2L, our online (web-enhanced) course delivery system. Your Username is the same as your VSCC
Student Email. Your Password is the same as your Pride Online password.
CALCULATORS: A scientific calculator is required. A graphing calculator is permitted (nothing
stronger than a TI-84), but not necessary. Hand-held computers and programmable computer-like
calculators (like the TI-89 or TI-92) are not permitted. Sharing a calculator between students is not
permitted on tests or quizzes.
HOMEWORK: Any student who has not completed the assigned homework before a scheduled quiz or
test will be at a distinct disadvantage, and will be graded more harshly. For those who have completed
all relevant homework by its due date, there will be EXTRA CREDIT available on the next Test. Doing
the assigned homework is absolutely essential for students to learn the skills necessary to successfully
complete this course. Any student who does not successfully complete at least 70% of the relevant
homework may be denied access to a quiz or test and is not eligible for any Extra Credit and/or Grading
Curve that might otherwise be available. For more information on Homework, see “Homework
Assignments” attached to the end of this syllabus. NOTE: Doing the online Mod Checks and online
Discussions is NOT REQUIRED in this class.
5
QUIZZES: All quizzes will be online (multiple choice and/or short answer). Quiz problems must be
worked on paper with answers submitted online to the instructor by the stated deadline. The textbook,
homework, and course notes may be used as a resource when doing a quiz, but assistance from
another person is not permitted.
On the designated quiz date, go to https://elearn.volstate.edu and log in to D2L. Your Username is the
same as your VSCC Student Email. Your Password is the same as your Pride Online password.
A score of zero will be assigned for each quiz not completed and submitted by the stated deadline.
Each student's lowest quiz grade will be dropped. Credit may be given for a late quiz at the
discretion of the instructor, provided the student contacts the instructor in advance to offer a legitimate
explanation and request an extension.
TESTS: There will be four major tests (non-cumulative) and a comprehensive final exam. Tests 1, 3,
and 4 will be online, but Test 2 and the Final Exam will be done on paper in the classroom. Students
are required to be present for all on-campus tests. A student who must miss a test due to an
emergency should make every attempt to notify the instructor prior to the time of the test. Assistance
from another person is never permitted on Tests. Anyone caught CHEATING on a test will receive a
grade of zero and may face other punitive measures.
MAKE-UP TESTS will be given only when the student's absence is due to an unexpected emergency
and is explained by documentation from the appropriate authority (doctor, judge, etc.). Make-up tests,
if allowed, will be harder than the regular test. A score of zero will be assigned for the missed test if
not excused by the instructor. Final exams must be taken at the scheduled time and will not be
returned to the student. There will be no exemptions from taking the Final Exam.
GRADES: The final numerical grade will be determined according to the following weighted
components.
Tests 1, 3, & 4 = 10% each
Quizzes (lowest dropped) = 15%
Test 2 = 15%
Homework = 10%
Final Exam = 25%
Participation (in class) = 5%
Letter grades will be assigned according to the following numerical grade intervals.
90.00
80.00
70.00
60.00
00.00
-
100 +
89.99
79.99
69.99
59.99
=
=
=
=
=
A
B
C
D
F
Favorable or unfavorable determination of borderline grades will be significantly influenced by
ATTENDANCE and HOMEWORK!
CLASS DISRUPTIONS: An affective mathematics learning environment will enhance (rather than
detract from) a student's (and instructor's) ability to concentrate. Therefore, it is the goal of this
instructor to provide all students with a relaxed, supportive classroom atmosphere free of unnecessary
distractions. Hence, any student who unnecessarily disrupts class (by way of persistent tardiness,
unauthorized talking, and the like) is subject to disciplinary action. Cell phones must be turned off
before coming to class.
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CHEATING: Students enrolled in any Volunteer State Community College Course will abide by the
policy regarding academic misconduct found in the Student Handbook at
http://www.volstate.edu/StudentHandbook/conduct.html paying particular attention to section C.(2).
TUTORIAL ASSISTANCE: Trained tutors are available in the Math Lab (Warf 123) or by calling
extension 3387. More information, such as Lab hours are posted on the Math Lab web site at
http://www.volstate.edu/MathScience/Lab/ . A student may contact the instructor during regular office
hours in Warf 100H or by calling (615)741-3215 or (615)452-8600 or 1-888-335-8722, extension 3386.
For online interaction with the instructor, use the email component of D2L at http://elearn.volstate.edu .
MATH 1720 Section V01 Online (Also MATH 1830 and MATH 1910): Students enrolled in the Online
section (V01) of these courses will get their primary instruction by viewing the animated online
PowerPoint presentations. Students enrolled in a traditional lecture section are encouraged to view
these presentations as needed for additional tutorial assistance. This may be done anywhere the
student has access to a personal computer linked to the Internet, including those in VSCC computer
labs. You may view any of these online presentations at http://www2.volstate.edu/obible .
HOMEWORK ASSIGNMENTS
MATH 1720
TEXTBOOK: Algebra and Trigonometry with Analytic Geometry (12th Ed.), Swokowski and Cole
For most of the homework assignments in this course you are required to use the Online Homework feature
of WebAssign. If you have not enrolled in WebAssign, go back to the course Orientation in D2L, click on
CONTENT, and click on "Enroll in WebAssign."
Homework assignments in WebAssign consist of algorithmically generated problems, tied to the course
textbook. Homework must be submitted by 11:59 pm (Central time) on the due date. The due date for each
Homework assignment is listed in the D2L Events Calendar. An individual student who occasionally may
need additional time to complete an assignment may obtain an automatic 2-day extension up to 7 days
after the due date. A second extension on an assignment may be granted manually in extreme cases. A
penalty of up to 5 points may be assessed for each extension. You may submit an assignment up to 3
times. Your last submission will be automatically graded and recorded. Homework grade totals will be
transferred from WebAssign to D2L Grades within a week after each major Test.
Lessons 6, 7, 23, and 30 must be done on paper and must be turned in to the Instructor. Any
student work that is to be faxed or scanned should be written in dark pencil or black, erasable ink. All graphs
must be done on graph paper (or copy paper, if done and printed from a graphing utility).
Lessons 10, 19, 28, and 35 (Reviews) and the Final Review are recommended (not required), and
are NOT to be turned in.
7
LSN
0
SECTION
NOTE:
Ch 1 = 6.x
Ch 2 = 7.x
Ch 3 = 8.x
ASSIGNMENT
COUNT
Study the Geometry Definitions Review. This consists of
definitions from Geometry that students are expected to know
throughout the course. Click on [COURSE CONTENT], then [VIEW
... PRESENTATION ...] in any of the Modules for a link to Lesson
0. Study the definitions. There is no homework to hand in for
Lesson 0 (Geometry Review) and no Keyword to submit.
1
6.1
WebAssign Homework 01
32
2
6.1
WebAssign Homework 02
22
3
6.1
WebAssign Homework 03
16
Quiz 1
Quiz 1 covering textbook section 6.1
4
6.2
WebAssign Homework 04
38
5
6.2
WebAssign Homework 05
13
6
6.2
Do this assignment on paper (no WebAssign submission).
14
p425 (36ab,37a,38b,39,40,42,43,45,49,52,54,55,56)
7
6.2
Do this assignment on paper (no WebAssign submission).
11
p425 (41,44,48,58,59,60,61,63,64,65,66)
8
6.2
WebAssign Homework 08
58
9
6.2
WebAssign Homework 09
26
Quiz 2
10
REVIEW
1
Quiz 2 covering textbook section 6.2
OPTIONAL: Do this assignment on paper (no WebAssign
submission).
p492 (1-18,21-24,28,29)
p410 (37a,43,44)
p429 (91)
TEST 1
Test 1 covering lessons 1 through 10
11
6.3
WebAssign Homework 11
46
12
6.3
WebAssign Homework 12
20
13
6.3
6.4
WebAssign Homework 13
42
14
6.4
WebAssign Homework 14
36
15
6.4
WebAssign Homework 15
33
Quiz 3
Quiz 3 covering textbook section 6.3 & 6.4
8
LSN
SECTION
16
6.5
WebAssign Homework 16
32
17
6.5
WebAssign Homework 17
37
18
6.5
6.6
WebAssign Homework 18
23
Quiz 4
19
REVIEW
2
ASSIGNMENT
COUNT
Quiz 4 covering textbook section 6.5 & 6.6
OPTIONAL: Do this assignment on paper (no WebAssign
submission).
p492 (19,20,25-27,30-56)
(45-56) Find the amplitude (or write none), period, phase shift,
and interval of one cycle. Then find equations of two successive
vertical asymptotes and the general equation of all asymptotes (or
write none). Using the approximate same scale on both axes,
label the x-axis and the y-axis, then plot 3 to 5 points, and graph
one cycle.
TEST 2
Test 2 covering lessons 11 through 19
20
6.7
WebAssign Homework 20
19
21
6.7
WebAssign Homework 21
20
22
6.7
7.1
WebAssign Homework 22
15
23
7.1
Do this assignment on paper (no WebAssign submission).
8
p506 (13,15,16,19,25,30,36,41)
24
7.1
7.2
Quiz 5
25
26
27
7.2
7.2
7.3
7.2
7.3
Quiz 6
WebAssign Homework 24
16
Quiz 5 covering textbook section 6.7 & 7.1
WebAssign Homework 25
48
WebAssign Homework 26
29
WebAssign Homework 27
11
Quiz 6 covering textbook section 7.2 & 7.3
9
LSN
SECTION
ASSIGNMENT
28
REVIEW
3
OPTIONAL: Do this assignment on paper (no WebAssign
submission).
COUNT
p495 (57-60,62,64,67)
p565 (1-6,9-14,17,18,23-29,45-50)
(23-29) Find the solutions of each equation that are in the
interval [0o, 360o).
TEST 3
29
30
Test 3 covering lessons 20 through 28
7.4
WebAssign Homework 29
7.4
Do this assignment on paper (no WebAssign submission).
20
9
p540 (4,15,17,25,26,31,33)
1. Express cos 64 in terms of sin 32 .
2. Express sin 185 in terms of cos 370 .
31
7.6
WebAssign Homework 31
15
32
7.6
WebAssign Homework 32
12
Quiz 7
Quiz 7 covering textbook section 7.4 & 7.6
33
8.1
WebAssign Homework 33
18
34
8.2
WebAssign Homework 34
25
Quiz 8
35
REVIEW
4
Quiz 8 covering textbook section 8.1 & 8.2
OPTIONAL: Do this assignment on paper (no WebAssign
submission).
p565 (7,8,15,16,19-21,51-56,59-70)
p629 (1-10,40,43)
TEST 4
FINAL
REVIEW
Test 4 covering lessons 29 through 35
OPTIONAL: Do this assignment on paper (no WebAssign
submission).
Download and print this Review; do all 35 problems (NOT to be
turned in). Also study your Tests (1 - 4) and Quizzes (1 - 8).
FINAL
EXAM
Comprehensive