Math
25: Unit 2
Unit 2 Target Date: Tuesday, February 10
Unit 2 DEADLINE Date: Friday, February 13
Note: The information on this page is
for the 7th edition of the textbook.
Click here for the 8th edition
information.
Click here for the 6th edition
information.
- Table of Contents:
- Topics
Study Guidelines
Unit Written Assignment
Unit Pretest and Exam Description
Checklist
Topics
The first part of Unit 2 continues the development of the trigonometric functions
by studying their value at general angles. In section 6.4, these values are computed
by using the reference triangle technique. In section 6.5, an alternative approach,
using the unit circle, is given. In fact, this actually provides a second alternative
definition of the trigonometric functions. It is very important that you learn both
approaches to the definition and calculation of trigonometric functions.
In the second part of Unit 2, you will see how trigonometry
can be used to solve a large variety of applications involving right triangles.
- Reference angles (6.4)
- Sign of trig functions in different quadrants
- Unit circle approach to the definition of trig functions (6.5)
- Properties of trig functions
- Applications involving right triangles (8.1)
Study guidelines for the 7th edition of
Sullivan's Algebra and Trigonometry
These reading and problem assignments are designed to help you learn the course
material. You should complete all of these problems, check your answers in the back
of the textbook, and get help with the problems that you missed. Most of the problems
are odd-numbered, so you can check the solutions in the Solutions
Manual.
The only way to learn mathematics is to do mathematics, so while these problems
will not be graded carefully, you will probably not do well in the course if you
do not complete these and check your work as described above. After completing these
problems, go on to the Unit Exam Description below and follow
directions.
- Section 6.4: Trigonometric Functions of General Angles
- Reading: section 6.4
Read and work through examples 1-8 and their matched problems.
You should become familiar with the signs of the various trig functions in the four
quadrants (this is actually easier to remember after you have covered section 7.5).
You should also become adept at using reference angles to compute the values of the
trig functions at a general angle.
- Practice Problems: 6.4 #11-19 odd, 21, 25, 31, 33-39 odd, 41, 45, 47,
49, 51, 57, 59, 61, 67, 69, 71, 75, 77, 81, 83, 87, 89, 91, 95, 97, 99, 101,
105, 107, 109, 111, 113, 115, 117
- Section 6.5: The Unit Circle Definition of the Trigonometric Functions
- Reading: section 6.5
Read and work through examples 1-3 and their matched problems.
This is a very important section. The trigonometric functions are defined a second
time in this section, this time in terms of the unit circle. This makes it easy to
see that each trigonometric function is actually a function whose domain is the set
of real numbers. It is crucial that you do not get locked into thinking of trigonometric
functions just in terms of triangles. Although the original definition is easy for
acute angles, this second definition is easier to use for general angles.
- You can download a copy of the unit circle
with the values of sine and cosine for the standard angles.
- Practice Problems: 6.5 #9-19 odd, 21, 27, 33, 35, 37, 41, 45, 51, 55,
57, 59, 61-97 odd
- Section 8.1: Applications Involving Right Triangles
- Reading: section 8.1
Read and work through examples 1-9 and their matched problems.
One of the primary uses of trigonometry is to solve problems involving right triangles.
In this section, a wide variety of such applications are demonstrated.
- Practice Problems: 8.1 #9, 13, 17, 19, 23-35 odd, 39, 41, 43, 53
- Supplementary material (optional):
- Student Solutions Manual
- CD lecture series (step-by-step video examples on CD)
- Section numbering on the CD's corresponds to the 7th edition of the textbook.
- Video lectures are available on reserve in the CR library.
- Section numbering on the video lectures corresponds to the 6th edition of the
textbook. Use the section correlation guide
to find the corresponding sections for the 7th edition.
- For tutoring help, visit the Prentice
Hall Math Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To
register, you will need to use your access code.
- Graphing
Calculator Help
Unit 2 Written Assignment
See Blackboard for Written Assignment and Blackboard Assignment.
Be sure to read and follow the 'General Guidelines' (look in Blackboard).
Unit 2 Pretest and Exam Description
After completing the above work, do the following:
- Read the exam description:
- This exam has 20 questions, and pretests count as 20% of your
grade.
- This exam has a one hour time limit.
- Many of the questions expect an exact answer. You can type pi for the number pi and sqrt(2) for the square root
of 2, etc.
- Other questions on this exam ask for an approximation instead
of an exact answer. These questions will ask you to give an answer "with an accuracy of at least two decimals after the decimal
point" (or possibly one decimal, or three decimals,
etc.). In this case, you would have to
enter at least two digits after the decimal point. For example, if you calculate
your answer to be 1.41421356237, then you could enter 1.41, 1.414, 1.4142, etc. When
you view your corrected exam, you will see that the "correct" answer is
1.41421356237
0.01.
The
symbol means "plus or minus", so anything within 0.01 of the first number
counts as correct.
- If a question does not ask for an approximation, then your answer
must be exact.
- If a question asks for an integer approximation, then your answer
must be an integer.
- Be sure to look under the entry box for the expected format of
the answer.
- Some problems expect an ordered pair, such as (1/2,sqrt(3)/2).
- Some problems expect a list, separated by commas, such as 1/2,sqrt(3)/2,sqrt(3). The values must be listed in the order requested in the problem.
- None of the problems in this course require answers in terms of
units, or dimensions (for example, "5
cm" or "3 ft"). In particular, questions asking for radians or degrees do
not expect units (in fact, as noted on page 481, radian measure is a dimensionless
number). Thus, you should not write answers like "pi/4 radians" or "45
degrees". Just write "pi/4" or "45" instead (the problem
will tell you if you are supposed to use radians or degrees).
- If an angle measure doesn't say "degrees" or use the
degree symbol, then it is in radians.
- Make sure your calculator is set to the correct
mode (radians or degrees) for each question.
- Complete the online Unit
2 Pretest assignment. You may
use your book if you wish, and redo the pretest as many times as you like. Your pretest
score will be scaled -- each pretest counts equally, and they comprise 20% of your grade.
- Directions: At the testing
web site, choose Unit 2 Exam.
- The proctored unit exam must be completed by the deadline date listed at the
top of this page, and may be repeated under certain conditions.
Note: Remember that you can always go back and take
practice exams on this unit after the deadline has passed. In particular,
this will help you prepare for the midterm and final exams.
- Directions: At the testing
web site, choose "Unit 2 Pretest/HW" assignment. After
the deadline has passed, this exam will be available in practice mode.
Unit 2 Checklist
Make sure that you have finished the following items to complete
Unit 2:
- Read the material and do the
problems listed in the Study Guidelines. Use any of the listed supplementary
material to help you understand the concepts.
- Update your Reference Book as you study.
- Complete the Discussion Board assignment in Blackboard.
- Prepare for Quizzes in class.
- Complete the Unit Written
Assignment.
- Complete the online Unit
Pretest/HW assignment (read the exam description first).
- Complete the online proctored Unit
Exam.
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