Math
25: Unit 1
Unit 1 Target Date: Thursday, January 29
Unit 1 DEADLINE Date: Tuesday, February 3 CHANGED TO: Friday, Feb. 6
Note: The information on this page is
for the 6th edition of the textbook.
Click here for the 7th edition
information.
- Table of Contents:
- Topics
Study Guidelines
Unit Written Assignment
Unit Pretest and Exam Description
Checklist
Topics
Unit 1 begins with a discussion of angles and various ways
to measure angles: radians, decimal degrees, and degrees-minutes-seconds.You are probably familiar with degrees, but in mathematics it is
more convenient to use radians. You will also learn to convert between the three
measurements.
The six trigonometric functions are then defined in terms
of right triangles (in Unit 2, you will learn a second approach to the definition
in terms of the unit circle). You will also learn how to compute the exact
values of these functions at certain angles, and approximations at more general angles.
It is Math Department policy that students should be able to compute the exact values
of all the circular (trigonometric) functions at the "standard" angles,
i.e., all multiples of pi/6 and pi/4 radians and 30 and 45 degrees.
Finally, you will also learn some of the basic identities that are satisfied by
the trigonometric functions.
- Angles and their Measure (7.1)
- Radians
- (Decimal) degrees
- Degrees-minutes-seconds
- Conversions between radians and degrees for standard angles (all multiples of
pi/6 and pi/4 radians and 30 and 45 degrees)
- Conversions between radians, (decimal) degrees, and degrees-minutes-seconds for
general angles
- Applications:
- connection between radians and lengths of arcs
- areas of sectors of circles
- circular motion
- Definition of trigonometric functions in terms of right triangles (7.2)
- Fundamental identities of trigonometric functions (7.2)
- Exact evaluation of trigonometric functions at standard acute angles (0, pi/6,
pi/4, pi/3, and pi/2) (7.3)
- Approximate evaluation of trigonometric functions with a calculator (make sure
your calculator is set to the correct mode!) (7.3)
Study guidelines for the 6th 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 collected or graded, 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 7.1: Angles and Their Measure
- Reading: section 7.1
Read and work through examples 1-8 and their matched problems.
You should know the relationships between arc length and radians and between degrees
and radians. Also, you should become very familiar with the "standard"
angles given in Table 1.
- Practice Problems: 7.1 #1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37,
39, 45, 47, 53, 57-79 odd, 81, 82, 85, 87, 89, 91, 93, 95, 97, 99
- Additional examples and exercises on circular
motion
- Section 7.2: Right Angle Trigonometry
- Reading: 7.2
Read and work through examples 1-7 and their matched problems.
You should know identities (1)-(7).
- Practice Problems: 7.2 #1-25 odd, 27, 29, 33, 35, 41, 43, 45, 47, 49,
57, 59
- Section 7.3: Computing the Values of Trigonometric Functions of Given
Angles
- Reading: 7.3
Read and work through examples 1-6 and their matched problems.
You should know the values of all of the trig functions at the standard angles listed
in Table 3.
- Practice Problems: 7.3 #1-23 odd, 25, 29, 33, 37, 39, 43, 47, 51
- 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.
Use the section correlation guide to find
the corresponding sections for the 6th edition.
- Video lectures are available on reserve in the CR library.
- Section numbering on the video lectures corresponds to the 6th edition of the
textbook.
- 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 first obtain an access code from me.
- Graphing
Calculator Help
Unit 1 Written Assignment
See Blackboard for Written Assignment and Blackboard Assignment.
Be sure to read and follow the 'General Guidelines' (look in Blackboard).
Unit 1 Pretest and Exam Description
After completing the above work, do the following:
- Before taking Unit Exam #1, you should have completed the Online Testing Practice.
If not, then do so now.
- Read the exam description:
- This exam has 25 questions, and will count 20 points toward 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.
- 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
1 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 to 5 points maximum.
- Directions: At the testing
web site, choose the Unit 1 Pretest.
- The pretest must be completed by the deadline date listed at the top of this
page.
However, you may redo the pretest as many times as you like before the deadline date.
Your best score counts, and it will be rescaled to 5 points maximum.
- See the instructions for pretests.
- If you are having trouble with any of the problems listed above
or on the pretest or practice exams, make use of the help resources listed on the
Help page.
- Make arrangements with your proctor to take the online proctored
Unit 1 Exam
assignment (see the instructions
for proctored exams). Remember
to bring identification, and remember that you will not be able to take the unit
exam after the deadline date given at the top of this page. You
may NOT use your book or notes on this exam.
- Directions: At the testing
web site, choose Unit 1 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. See the Detailed
Schedule page for specific rules.
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 1 Practice Exam. After
the Unit deadline has passed, this exam will be available in practice mode.
Unit 1 Checklist
Make sure that you have finished the following items to complete
Unit 1:
Math 25 home page