Harwell_ACP

Question 1

Which of the following is a trigonometric equation?
a. 2 = 4
b. + 7 = 12
c. sin + cos()
d. sin + tan = 0

13

Question 2

What is arcsin(sin ) equal to?
a.
b.
c. 0
d. sin

14

Question 3

Name the algebraic technique(s) used to solve sin2() − 1 = 0. Note that they must be in order of use.
a. Completing the square, Factoring, Zero Product Principle
b. Factoring, Completing the square, Zero Product Principle
c. Factoring, Zero Product Principle
d. Zero Product Principle, Factoring

15

Question 4

What is the identity used to solve the following equation sin2() + cos2() + sin = −1?
a. Sum Identity
b. Power Reduction Identity
c. Factoring Identity
d. Pythagorean Identity

16

Example

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 cos2 + cos − 1 = 0

Solution

Strategy
Note that the form of the equation is quadratic.

2 cos2 + cos − 1 = 0
2 + + = 0

Quadratic in Form Factor Set factors equal to zero Solve

17

Example

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 cos2 + cos − 1 = 0

Solution
2 cos2 + cos − 1 = 0

2 cos − 1 cos + 1 = 0 Factoring

2 cos − 1 = 0 or cos + 1 = 0 Zero Product Principle
or cos = −1 Solve
cos 1
=2

18

Example

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing. Here
2 cos2 + cos − 1 = 0

Solution

cos 1 or cos = −1
=2
Here
5
= 3 ,3 =

Here 19

Example

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 cos2 + cos − 1 = 0

Solution (Check) = 2 cos2 + cos − 1

= , , 5
3 3

= 0

20

Exercise

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 sin2 + sin − 1 = 0

Post-Assessment

Description
Have the students switch papers and grade them for correctness as you explain the
answers. Then have them give the papers back to the original student for them to look at.
The students can then decide for themselves is the objectives have been met.
Classroom Assessment Technique (CAT) – Student Marking

22

Question 1

Which of the following is a trigonometric equation?
a. 2 = 4
b. + 7 = 12
c. sin + cos()
d. sin + tan = 0 Correct

23

Question 2

What is arcsin(sin ) equal to?
a. Correct
b.
c. 0
d. sin

24

Question 3

Name the algebraic technique(s) used to solve sin2() − 1 = 0. Note that they must be in order of use.
a. Completing the square, Factoring, Zero Product Principle
b. Factoring, Completing the square, Zero Product Principle
c. Factoring, Zero Product Principle Correct
d. Zero Product Principle, Factoring

25

Question 4

What is the identity used to solve the following equation sin2() + cos2() + sin = −1?
a. Sum Identity
b. Power Reduction Identity
c. Factoring Identity
d. Pythagorean Identity Correct

26

Exercise

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 sin2 + sin − 1 = 0

Solution

Strategy
Note that the form of the equation is quadratic.

2 sin2 + sin − 1 = 0
2 + + = 0

Quadratic in Form Factor Set factors equal to zero Solve

27

Exercise

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 sin2 + sin − 1 = 0

Solution
2 sin2 + sin − 1 = 0

2 sin − 1 sin + 1 = 0 Factoring

2 sin − 1 = 0 or sin + 1 = 0 Zero Product Principle
or sin = −1 Solve
sin 1
=2

28

Exercise

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 sin2 + sin − 1 = 0

Solution Here

sin 1 or sin = −1
=2
Here
5
= 6 ,6 = 3
2

Here 29

Exercise

Solve the equation on the interval 0 ≤ < 2. Then verify the results using graphing.
2 sin2 + sin − 1 = 0

Solution (Check) = 2 sin2 + sin − 1

= , 5 , 3
6 6 2

= 0

30

Summary

Description

A small discussion and cliffhanger about what we will be studying next
(Applications)

31

A new land for us to explore …

What adventure await us in our new land of trigonometry? 32
What could we use our equation solving skills for?
To be continued …

Personal
Reflection on

My ACP
Experience

Reflective Essay for ACP

Lone Star College – University Park

Guy Harwell

Introduction

First, I would like to say that I have enjoyed the adjunct certification program. It has been a beneficial
program to help me with a plan to organize my lessons around for the classes that I am instructing.

I have also enjoyed the company of other instructors and appreciate the different views that they bring
to the program. Having instructors from different disciplines is also a strength of the program and is a
wonderful idea for increasing our contact with points of view from others outside of our departments.

As a suggestion for the program I would like to see more full-time faculty (from different disciplines)
and administration come in to talk with the adjunct instructors about with their ideas, opinions, and
experiences from working as a full-time instructor or administrator.

I believe that this will help us the adjunct instructors hear the opinions and suggestions of the full-time
instructors on their way of instruction and to help the adjunct instructors have a better understanding of
the challenges that full-time instructors and administrators face in their daily work.

Question 1

What value/ knowledge/ insights have you gained from the Adjunct Certification Program?

The program has presented many ideas that has increased my knowledge of instruction. One such idea
is BOPPPS as an overall way to structure individual lessons. Another such ideas are using different
technologies in the classroom to increase student engagement (such as Poll Everywhere).

An insight that I will take away from the program is that there are many suggestions to different issues
that we are faced with in the classroom and that as instructors we are actively trying to answer the
different challenges that we are faced with.

Question 2

How have you incorporated the knowledge gained into your classroom?

I have incorporated several ideas that I learned in the Adjunct Certification Program into my classroom.

• The overall structure of BOPPPS as a way form to construct my instruction around.
• The use of technology to increase engagement of the students.
• Using the pre-assessment of BOPPPS to help students to prepare for the lecture

These are some of the ideas that I have learned in the program that I will (or already have) be using in
the classroom.

I do plan on incorporating more ideas and suggestions that I have learned in the program I the future.

Page 1 of 3

Question 3

How has this program made you a more effective instructor?

The program has made me a more effective instructor by helping me to be more aware of how I
instructor the course and how I present the course to the students. Also, I feel that the interaction with
the other instructors has really given me new points of view on my own feelings and ideas about
instruction.

It is in the last point that I feel that I have really grown in my effectiveness as an instructor. The
experiences and ideas that the adjuncts instructors bring are of direct relevance to what I also face in my
daily work as an adjunct instructor and having a form for me to directly interact with them has helped
me.

One idea that has made me more effective is the use of the Bridge in BOPPPS. This has helped me to
gain the attention of the class as an opener to the lesson.

Question 4

What suggestions do you have for further professional development opportunities?

One suggestion that I have for further professional development opportunities is to have a regular form
that adjunct instructors can speak with and hear the opinions of faculty instructors and administration
on topics such as the effectiveness of certain classroom techniques.

I also would like to see more programs that are discipline specific and more information on the specific
goals of each department. The idea that we have adjunct instructors from different departments is good
for gaining different points of view, but there are some issues that are discipline specific and are difficult
to approach in a general way. These topics really need a person who knows the discipline and is able to
talk to each challenge using the ideas that follow the discipline itself.

Also, more professional training on faculty instructor interview. Such topics such as resume writing and
interviewing skills could be addressed.

Conclusion

In conclusion I would just like to say that I really did enjoy the program and hope to continue my
professional training in programs like the Adjunct Certification Program. As a further suggestion for the
program I would have liked to see different techniques to classroom management and to create lessons
that are not as ridged and leave more room for creativity for the instructor and student in the
classroom.

In addition to this I would like to see more discipline specific programs that can address the issues faced
by instructors in the discipline. This is where faculty and administration could be involved in the process
giving suggestions and ideas to the adjunct instructors. Such a program could also be centered on how
to land a faculty position which is a major concern of many adjunct instructors.

Lastly, I would like to say that I am very happy that Lone Star College – University Park has programs like
this one and seeks to help its instructors to improve in their craft. I would like to thank all of the people

Page 2 of 3

that participated (other instructors and those who helped plan and execute the program) and of course
Bruce. Thank you.

Page 3 of 3