COURSE OUTLINE
COURSE: INTRODUCTION TO TRIGONOMETRY
COURSE NO.: MATH 116
SEMESTER: Spring, 2003
INSTRUCTOR: E. Peifer
PHONE:
687-5224
E-MAIL:
peifere@sunyulster.edu
WEB SITE: http://people.sunyulster.edu/peifere
TEXTBOOK: Cohen, Precalculus, FIFTH edition (same text as in MAT 160)
OFFICE HOURS:
Room Bur 107A (Burroughs Science Building)
MWF: 8:30-9:30
TR: 8:15-9:15 (or any free time)
COURSE OBJECTIVES FOR MAT 116
At the completion of this one credit course, the student will:
(1)
Know the definitions and properties of the six trigonometric
functions of any angle in degree and radian modes;
(2)
be able to apply the trigonometric functions to the right
triangle and to use the laws of sines and cosines to the general
triangle;
(3)
know and be able to work with the fundamental trigonometric
identities and how to use these identities in elementary
trigonometric proofs.
TEACHING AND EVALUATION OF MAT 116
The primary mode of instruction for Mat 116 is seven video tapes which
cover the basics of right triangle trigonometry. The tapes will be viewed
on campus and will follow chapter 6 and parts of chapter 7 of the
Precalculus (Cohen) textbook. The instructor will be responsible for the
coordination of the course materials and the evaluation of the students.
The student will be required to pass a final exam which will be offered any
time before the final exam period. Students who are concurrently taking Mat
160 with this course must complete the course by mid-semester. The final
grade will be based on the student's performance on the final exam. The
correspondence between final average and final grade is attached.
Important:
Before taking the final be sure to pick up a review packet
which contains problems (including answers) which are very similar to those
included on the final. These packets can be obtained from me or our
faculty secretary.
HAVING PROBLEMS?
If you run into any difficulties either with the course content or
materials, procuring the videos, time-management problems, etc. please see
me in my office, or contact me by phone or e-mail as soon as possible. I'm
sure I assist you. I do answer calls and e-mails.
OUTLINE FOR MAT 116
I.
LESSON I - INTRO TO GEOMETRY AND THE RIGHT TRIANGLE TRIG. FUNCTIONS
A. Angles
1. Definition
2. Special angles: right, obtuse, acute
3. Degree measurement
4. Angle of elevation and depression
B. Circles
1. Center, radius, diameter, circumference, arcs and formulas
2. Equation of a circle, including the unit circle
C. Polygons
1. Basic definition
2. Regular polygons - quadrilaterals, pentagons, hexagons, etc.
D. Triangles
1. Equilateral, isosceles, right, scalene
E. Properties of triangle
1. Right triangle properties
a. Complementary acute angles
b. Similar right triangles determined by one acute angle
c. Proportional properties of similar right triangles
d. Right triangles being building blocks for isosceles and
equilateral triangles, as well as rectangles and regular
polygons
F. Definitions of the six trigonometric functions based on similar
right triangles
1. Sin, Cos, Tan, Csc, Sec, Cot functions
2. Reciprocal relationships
3. Importance of mode when using a calculator
II. LESSON II - INTRO TO RIGHT TRIANGLE TRIG., TRIG. VALUES OF SPECIAL
ANGLES
A. Conventional notation used in right triangles for angles and sides
B. Pythagorean theorem
C. Determination of six trig rations given two sides of a right
triangle
1. Use pictures and non-pictorial problems
D. Trig. ratios of special angles
1. 30-60-90 degree right triangle
2. 45-45-90 degree right triangle
3. Exact trig values of 30, 45 or 60 degree angles
E. Using the calculator
1. Mode check (degrees)
2. Evaluation of sec, csc and cot using calculator
III.
A.
B.
C.
LESSON III RELATIONSHIPS BETWEEN TRIG. FUNCTIONS, INTRO. TO TRIG
IDENTITIES, SOLVING TRIANGLES
Given the value of one trig function, find one or more values from
the remaining five trig functions using right triangles
Intro to the following key trig identities:
sin2  + cos2  = 1
1. Reciprocal identities: tan  = 1/cot , csc  = 1/sin ,
sec  = 1/cot 
2. tan  = sin /cos  and cot  =
cos /sin 
o
3. Co-function identities cos(90
) = sin ,
cot(90o - ) = tan , csc(90o - ) = sec 
Simplification of trig expressions using the above identities
IV. LESSON IV - (1 hr. 20 min) TRIG IDENTITIES, SOLVING TRIANGLES,
DEFINITION
OF TRIG FUNCTIONS OF ANY ANGLE USING THE UNIT CIRCLE,
REFERENCE ANGLES.
A. Simplification of a quotient using trig identities (homework)
B. Solution of "practical" problems using sin, cos, tan
C. Definition of sin and cos of any angle using unit circle
1. Determination of reference angles in each of the four quadrants
2. Determination of the sign of the sin and cos in the quadrants
3. Working with negative angles and angles greater than 360o.
4. Patterns of the signs of sin and cos in each of the four
quadrants
5. Finding the sin, cos and tan for angles which are multiples of
90o.
6. Finding the tan, cot, sec and csc of any angle using quotients
and reciprocals
7. Finding the exact value of any trig function using angles which
are multiples of 90o, 30o, 60o, or 45o.
V.
LESSON V - SOLVING RIGHT TRIANGLES (homework), USING REFERENCE ANGLES,
AN INTRODUCTION TO PROVING TRIG IDENTITIES.
A. Three "practical" trig problems
B. Continuation of evaluating trig functions of any angle
C. Given the trig value of one trig function in any quadrant, find
the values of the other five trig functions using the principal
trig identities
D. Strategies and examples of proving a given trig identity
VI. LESSON VI - TRIG IDENTITIES, FINDING SYMBOLIC RELATIONSHIPS BETWEEN
TRIG FUNCTIONS, INTRODUCTION TO RADIAN MODE
A. Given the trig value (possibly symbolic) of one trig function in
any quadrant, find the values of the other five trig functions
using the principal trig identities
B. Two more trig identities
C. Developing the concept of the radian
1. Emphasizing the need to measure angles using a length
2. Definition of radian using the unit circle
3. Geometric interpretation of radian
4. Conversion between radians and degrees using proportions,
formulas and in certain special circumstances, the unit circle
5. Using radians on a calculator
VII. LESSON VII - CONVERSION FROM DEGREES TO RADIANS, WORKING DIRECTLY IN
RADIAN MODE, USING RADIANS IN FORMULAS, A FEW MORE TRIG IDENTITIES
A. Conversion to and from degrees and radians
B. Evaluating trig functions using multiples of ð, ð/2, ð/4, ð/3, and
ð/6 using the unit circle and reference angles in radian mode
C. Using radians in the formulas s = r and A = (1/2)r2 
D. Introduction of the identities:
1. sec2  = tan2  + 1, csc2  = sec2  + 1
2. sin(-) = -sin(), cos(-) = cos(), tan(-) = -tan()
E. Using the above identities to find relationships of trig functions
in any quadrant in radian mode
ASSIGNMENTS TO ACCOMPANY MAT 116 TAPES:
All page numbers and problems refer to Cohen, Precalculus, West Publishers,
fifth Ed. (Our Precalculus, Mat 160, textbook).
TAPE 1: READING:
pages 357-362
Learn the definitions of the six trigonometric functions. It might
also be helpful to review the pythagorean theorem, c2 = a2 + b2 for
right triangles before viewing tape 2.
TAPE 2: READING:
PROBLEMS:
TAPE 3: READING:
PROBLEMS:
TAPE 4: READING:
PROBLEMS:
pages 357-362
page 364-365:
1-33(odds)
pages 367-372
pages 372-378: 1, 3, 5, 19-29(odds), 35-47(odds)
pages 374-378, 383-391
pages 379-380: 1-13(odds)
pages 391-392: 1-39(odds), 40
TAPE 5: READING:
PROBLEMS:
TAPE 6: READING:
PROBLEMS:
TAPE 7: READING:
PROBLEMS:
pages 395-398
pages 399:
1-31(odds)
pages 408-415
pages 415-416
1-11(all), 31-37(odds)
pages 417-418, 427-434
pages 422:
1-4(all)
pages 435-436:
37
(know arc length formula)
1-9(odds), 13, 15, 17, 25, 27, 31, 33,