Harwell_ACP

Math 1316: Trigonometry Course Material:

Instructor Harwell You need to be working
Email: [email protected] out of this!

Some axioms (rules) for the class Homework is done on MyMathLab

1. Use your student email for communications. “Transcendental
2. Be polite and respectful of others. [numbers], They
3. No cell phones in class. transcend the power
of algebraic methods.”
Properties (policies) for the Exams
L. Euler
1. No make-up exams
2. Grade Replacement Policy

• Your final exam grade can replace the zero from the missed exam.
• This grade replacement is only applied one time.
• The lowest exam grade can be replaced by the final exam if it is higher.

Your grade will be Details Percent of Final Remember, any day you
determined by the Average get to do math is a great
following Homework assignments day!
In-class and/or online quizzes 15%
Assignments Major exams
Cumulative final exam 55%
Major Exams 30%

Final Exam

Total: 100%

Second P
Guy Harwell

COURSE: MATH 1316 Trigonometry
Lesson Title: Trigonometric Identities
Course Student Learning Outcome:

1. Prove trigonometric identities.

Learning Objectives (these should be the ones you wrote in Module 1): By the end of this lesson, students will be able to
1. Use Algebra to Simplify Trigonometric Expressions
2. Establish Identities

Participatory Learning: Learner Activities Lesson Materials
Time Instructor Activities

10 min Review solving algebraic equations Have students solve algebraic equations. Slides with exercises
10 min Review fundamental trigonometric identities Have students find variations of fundamental identities by Slides with fundamental
solving exercises. Write fundamental identities on note identities and exercises
10 min Mini-Lecture showing examples. cards and have students say identities to cards.
Have students participate by asking them for the next step. Slides with notes and
15 min Help students practice solving exercises by helping exercises
the groups individually. Put students into groups and have the groups work Slides with exercises
exercises.
See Attached PPT

BOPPPS LESSON PLAN

COURSE: Trigonometry

Lesson Title: Solving Trigonometric Equations (Single and Quadratic Form)

Bridge: How will you gain learner interest and set the stage for the lesson?

Start with a question on a quadratic equation such as x^2 + 4x + 2 = 0 and ask them if they remember how to solve such an equation and do they know why

they solve this equation in the manner that they do. (See slide 4 from lecture)

Estimated time: 10 minutes

Course Student Learning Outcome:

Solve trigonometric equations.

Learning Objectives: By the end of this lesson, students will be able to

1. Solve trigonometric equations involving trigonometric functions (Bloom level 3 - Application)

2. Solve trigonometric equations that are quadratic in form. (Bloom level 3 - Application)

Pre-Assessment: How will you assess learner prior knowledge of the topic? This could possibly tie to the student preparation strategy you developed.

Ask students to write down their answers to the question posed in the Bridge part of the lesson and have them focus on the why part of the question.

Estimated time: 10 minutes

Participatory Learning:

HIGHLIGHT AND LABEL THE FOLLOWING:

• 4 questions with Bloom’s level identified

• New instructional technology you are trying

• At least one classroom assessment technique (CAT)

Time Instructor Activities Learner Activities Lesson Materials

10 min Answer question posed in Bridge activity Check answers from Pre-Assessment PowerPoint, OneNote

15 min. Present poll questions, discuss poll answers Write down poll questions, participate in discussion Poll Everywhere;PowerPoint

10 min. Examples

15 min. Walk around and look at answers Solve exercises

Post-assessment: How will you assess if objectives have been met?

Classroom Assessment Technique (CAT) – Student Marking

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.

Estimated time: 15 minutes

Summary: How will you close the lesson? Present a question for next class period. What could we use this knowledge of solving equations for?

Estimated time: 5 minutes

ATTACH ANY LESSON MATERIALS (SLIDES, HANDOUTS, ETC.)

1. Which of the following is a trigonometric equation? (Bloom: Understand/ Classifying)

2. What is arcsin(sin()) equal to? (Bloom: Remember/ Recognizing)
3. Name the algebraic technique(s) used to solve sin2() − 1 = 0. Note that they must be in order of use. (Bloom: Apply/ Executing)
4. What is the identity used to solve the following equation sin2() + cos2() + sin() = −1?( Bloom: Create/ Producing)

ACP Showcase Portfolio

Name: Guy Harwell
Discipline: Mathematics

Date: 11/6/2017

Table of Contents

• Student Preparation Strategy
• BOPPPS lesson-be sure to highlight the following:

• CAT
• Questions
• Technology

• Reflection

Student Preparation Strategy

1. Students will read appendix section A.4 in the textbook and
complete exercises 5 – 12 (Concepts and Vocabulary)

2. Students will be expected to turn in worked out examples from text
via D2L.

Trigonometry

Math 1316

By Instructor Harwell 4

Section 3.8

Trigonometric Equations II
BOPPPS

By Instructor Harwell 5

OBJECTIVES

Course Student Learning Outcome:
Solve trigonometric equations.

Learning Objectives: By the end of this lesson, students will be able to
Solve trigonometric equations involving trigonometric functions (Bloom
level 3 - Application)
Solve trigonometric equations that are quadratic in form. (Bloom level
3 - Application)

Bridge (Story Time)

Description
Start with a question on a quadratic equation such as x^2 + 4x + 2 = 0 and ask them
if they remember how to solve such an equation.

7

In a land not so far away ...

In the land of algebra there lives many functions. Some have names such as linear and exponential, but there
is one function that often stands out amongst the rest.

In this land of algebra lives a function. A funny function by linear standards for it has a quadratic form.

Who
am I?

?

What is this form you ask? Well that is what I was hoping you could help me with.

8

Pre-Assessment (Who Am I?)

Description
Ask students to write down their answers to the questions. Have them think about how
and why they answer the questions the way they did.
Have students discuss in groups and walk around and see answers.

9

Who am I?

Q1: What is the general form of a quadratic function?
Q2: Does the equation 2 + 4 + 2 = 0 have this form? How do you know?
Q3: What are the steps to solve an equation such as 2 + 4 + 2 = 0? What is the name of each step?

10

Participatory Learning

Description
Question and answer session with poll.
Have students write down and answer questions as each slide appears. Then have the
students answer the poll.
Technology – Poll Everywhere, PowerPoint, Use of Tablet

11

Instructions

1 2 3 4

Write down the Write down your Website: Go to Text messaging: Text
questions answers PollEv.com/gharw647 GHARW657 to 22333
to join the session
then text a, b, c, d

12

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

Formal Assessment

Instructor: Guy Harwell

Questions

1. (Bloom: Understand/ Classifying)
Which of the following is a trigonometric equation?
a. 2 = 4
b. + 7 = 12
c. sin() + cos()
d. sin() + tan() = 0 (correct)

2. (Bloom: Remember/ Recognizing)
What is to arcsin(sin())?
a.
b. (correct)

c. 0
d. sin()

3. (Bloom: Apply/ Executing)
Simplify the following: sin2() − 1 = 0. Bonus: Name the algebraic technique you are using to
simplify with.

Solution: (sin() + 1)(sin() − 1) = 0

Bonus: Factoring Method - Difference of Squares

4. (Bloom: Create/ Producing)
Create a trigonometric equation that you would need to use a Pythagorean Identity to solve and
solve it.

Solution: There are many answers that could be correct.

Example: sin2() + cos2() + sin() = −1
1 + sin() = −1
sin() = 0
= 0

Solving Trigonometric Equations

Instructor: Guy Harwell
Student: __________________

Category/ Points 3 2 1
Correctness Uses correct solving Uses correct solving Uses correct solving
method, no calculation method, some method, calculation
Writing errors, calculation errors errors,
Clean, readable, Clean, readable Readable
Efficiency communicates using
Remark correct mathematical solving efficiency issues poor solving efficiency
notation.
understands how to Good Needs Work
solve efficiently
Excellent

ACP Showcase Portfolio

Name: Guy Harwell
Discipline: Mathematics

Date: 11/6/2017

Table of Contents

• Student Preparation Strategy
• BOPPPS lesson-be sure to highlight the following:

• CAT
• Questions
• Technology

• Reflection

Student Preparation Strategy

1. Students will read appendix section A.4 in the textbook and
complete exercises 5 – 12 (Concepts and Vocabulary)

2. Students will be expected to turn in worked out examples from text
via D2L.

Trigonometry

Math 1316

By Instructor Harwell 4

Section 3.8

Trigonometric Equations II
BOPPPS

By Instructor Harwell 5

OBJECTIVES

Course Student Learning Outcome:
Solve trigonometric equations.

Learning Objectives: By the end of this lesson, students will be able to
Solve trigonometric equations involving trigonometric functions (Bloom
level 3 - Application)
Solve trigonometric equations that are quadratic in form. (Bloom level
3 - Application)

Bridge (Story Time)

Description
Start with a question on a quadratic equation such as x^2 + 4x + 2 = 0 and ask them
if they remember how to solve such an equation.

7

In a land not so far away ...

In the land of algebra there lives many functions. Some have names such as linear and exponential, but there
is one function that often stands out amongst the rest.

In this land of algebra lives a function. A funny function by linear standards for it has a quadratic form.

Who
am I?

?

What is this form you ask? Well that is what I was hoping you could help me with.

8

Pre-Assessment (Who Am I?)

Description
Ask students to write down their answers to the questions. Have them think about how
and why they answer the questions the way they did.
Have students discuss in groups and walk around and see answers.

9

Who am I?

Q1: What is the general form of a quadratic function?
Q2: Does the equation 2 + 4 + 2 = 0 have this form? How do you know?
Q3: What are the steps to solve an equation such as 2 + 4 + 2 = 0? What is the name of each step?

10

Participatory Learning

Description
Question and answer session with poll.
Have students write down and answer questions as each slide appears. Then have the
students answer the poll.
Technology – Poll Everywhere, PowerPoint, Use of Tablet

11

Instructions

1 2 3 4

Write down the Write down your Website: Go to Text messaging: Text
questions answers PollEv.com/gharw647 GHARW657 to 22333
to join the session
then text a, b, c, d

12