Download Math 1060 Teaching Tips

Math 1060 Teaching Tips
1) Save on photocopying at the beginning of the semester!
The standard Math 1060 syllabus posted on the Math Department website no longer contains a
place for instructor information. Instead, a one page information sheet is available for
instructors to enter their contact information and specific grading policies.
2) Emphasize mastery of trig values of “special angles” in the first weeks of the semester
It is important that students learn the values of the trigonometric functions as soon as
possible in the semester. They will use these throughout the course and they are
expected to find these values without the use of the calculator. Try giving frequent,
brief, in class quizzes to encourage students to learn these values as soon as possible.
You may want to try a “fill in the box type”. For example
α in degrees
0
α inradians
sinα
cosα
tanα
30
45
60
90
3) Use online resources for “handouts”
There are many websites that have valuable resources. You can direct students to these
sites…it is not necessary to have printed handouts for all resources. Try
EmbeddedMath.com . There are some nice sheets on special angles, the unit circle and
special graph paper under “Free Math Worksheets”. Use MyPage to post your own
materials for students to access and print.
4) Encourage students to memorize a few basic identities and be able to quickly derive
others.
Please see the last two pages for an example of a handout that emphasizes the most
important identities for students to know in this course. (Please note that students should
also know the cofunction identities). This handout is also posted for students and faculty at
http://slccmathdepartment.yolasite.com .
**Notes or formula cards are not allowed on tests!**
5) Provide some extra feedback on verifying identities.
Assign and collect the “Verifying Identities Worksheet” to provide feedback before the
exam. Students usually need some extra guidance with this new and difficult concept.
6) Review section 6.1 (complex numbers in standard form) as needed.
Section 6.1 is not listed on the class calendar, but review problems are listed in the
suggested homework exercises. You may want to spend a few minutes of class time in
rapid review and/or assign the students to review the material on their own.
7) Encourage students to use the departmental test reviews.
Test reviews posted at http://slccmathdepartment.yolasite.com will help students prepare
for the midterm exams as well as the departmental final.
8) Require students to post a 1060 signature assignment in their SLCC eportfolio.
Students will be asked to complete a project and post it to their General Education
eportfolio along with a piece of reflective writing.
Trig Identity Handout for Math 1060
(The more stars, the more important the identity.)
***Basic identities:
sin 
cos 
cos 
cot  
sin 
tan  
1
cos 
1
csc  
sin 
sec  
cot  
1
tan 
***Pythagorean identities:
2
2
sin 2   cos 2   1 Be able to recognize and quickly derive: 1  cot   csc 
2
2
tan   1  sec 
** Even-Odd identities:
Cosine and secant are EVEN functions:
All the rest are ODD functions:
cos( x)  cos x
sec(  x)  sec x
sin( x)   sin x
csc( x)   csc x
tan( x)   tan x
cot( x)   cot x
Sum and difference identities:
*** cos(   )  cos  cos   sin  sin 
Use even-odd to derive the difference identity:
cos(  (  ))  cos  cos(  )  sin  sin(  )
** cos(   )  cos  cos   sin  sin 
*** sin(   )  sin  cos   cos  sin 
Use even-odd to derive the difference identity:
sin(  (  ))  sin  cos(  )  cos  sin(  )
** sin(   )  sin  cos   cos  sin 
Double Angle Identities:
sin(2 x)  sin( x  x)
 sin x cos x  cos x sin x
(apply sum identity)
** sin(2 x )  2sin x cos x
cos(2 x)  cos( x  x)
 cos x cos x  sin x sin x
(apply sum identity)
 cos 2 x  sin 2 x
2
2
* * cos(2 x)  cos x  sin x
cos 2 x  sin 2 x
 1  sin 2 x  sin 2 x (apply Pythagorean identity)
 1  2sin 2 x
2
** cos(2 x)  1  2sin x
cos 2 x  sin 2 x
 cos 2 x  (1  cos 2 x) (apply Pythagorean identity)
 2 cos 2 x  1
2
** cos(2 x)  2cos x  1
Half angle identities are really just a different way of looking at double angle identities.
Let u  2 x, then
u
2
 x . “Plug in” to the double angle identities then solve for either
sin  u2  or cos  u2  .
cos u  1  2sin 2  u2 
cos u  2cos 2  u2   1
2sin 2  u2   1  cos u
2cos 2  u2   1  cos u
sin 2  u2  
1  cos u
2
* sin  2   
1  cos u
2
sin 2  x  
1  cos 2 x
2
u
cos2  u2  
1  cos u
(“Power Reducing”-used in Calculus)
2
cos  u2   
cos 2  x  
1  cos u
Half Angle Identities
2
1  cos 2 x
(“Power Reducing”-used in Calculus)
2