Mr. Wolf
Thursday 1/8/09
Pre-Calculus
Grades 10-12
Unit 6: Analytic Trigonometry
Verifying Trigonometric Identities
Materials and Resources:
 Warm-up (1 per student)
 Verifying Trigonometric Identities Notes Sheet (1 per student)
 Verifying Trigonometric Identities HW Sheet (1 per student)
 Exit Ticket (1 per student)
PA Standards Addressed:
Instructional Objectives:
 Students will be able to verify identities by applying trigonometric identities,
adding fractions, factoring, squaring a binomial, and creating monomial
denominators.
Time
10 min
1 min
5 min
min
min
min
1 min
5 min
Activity
Warm-up
Agenda
Homework Check
Description
Pass out the Warm-up and review solutions.
Review the goals for the day.
Spot-check and instruct students to copy their
solution to pg. # onto the back of the Warm-up.
Collect and grade.
Review Homework
Present the HW solutions and answer any
questions.
Verifying
Modeling:
Trigonometric
Guiding:
Identities Notes Sheet Independent Practice:
Assessment:
Modifications:
Students with special needs…
Advanced students…
Pg. 387 #1-38
Modeling:
Guiding:
Independent Practice:
Assessment:
Modifications:
Students with special needs…
Advanced students…
Agenda
Revisit goals and identify whether they were met.
Conclusion
Pass out the Exit Ticket and collect at the bell.
Homework:
Verifying Trigonometric Identities HW Sheet (1 per student)
Lesson Reflection:
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Warm-up
Verifying Trigonometric Identities
Verify the identity cot 2 y(sec 2 y  1)  1 .
Steps to Solve:
1) Circle the more complicated side of the identity: cot 2 y(sec 2 y  1)
OR
1
2) Use Fundamental Trig Identities to change the first term of this complicated side:
3) Use Fundamental Trig Identities to change the expression in the parentheses:
4) Multiply the two new terms together:
Pre-Calculus/Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Warm-up
Verifying Trigonometric Identities
Verify the identity cot 2 y(sec 2 y  1)  1 .
Steps to Solve:
1) Circle the more complicated side of the identity: cot 2 y(sec 2 y  1)
OR
1
2) Use Fundamental Trig Identities to change the first term of this complicated side:
3) Use Fundamental Trig Identities to change the expression in the parentheses:
4) Multiply the two new terms together:
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Verifying Trigonometric Identities
Notes Sheet
Goal: To verify identities by applying fundamental trigonometric identities and
simplifying.
sec 2   1
Example: Verify the identity
 sin 2  .
2
sec 
Unfortunately, there is no well-defined set of rules to follow in verifying trigonometric
identities and the process is best learned through practice and experience. However, the
set of guidelines provided below can be useful when solving these problems.
Method 1: Applying Fundamental Trigonometric Identities
sec 2   1
Example: Verify the identity
 sin 2  .
sec 2 
Solution 1:
Solution 2:
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Method 2: Combining Fractions
Example: Verify the identity
1
1

 2 sec 2  .
1  sin  1  sin 
Method 3: Converting to Sines and Cosines
Example: Verify the identity tan x  cot x  sec x csc x .
Method 4: Creating a Monomial Denominator
Example: Verify the identity sec y  tan y 
cos y
.
1  sin y
Method 5: Factoring
Example: Verify the identity tan 4 x  tan 2 x sec 2 x  tan 2 x .
Method 6: Simplifying Both Sides Separately
cot 2 
1  sin 
Example: Verify the identity
.

1  csc 
sin 
Block: ______
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Verifying Identities HW
Directions: For each problem you must…
a. identify the more complicated side of the identity
b. identify the method used to verify the identity
c. identify all Fundamental Trigonometric Identities that needed to be applied
d. show the work used to verify the identity
Example: Verify the identity
tan x  cot x
 sec x .
cos x
More Complicated Side of Identity
Method Used to Verify Identity
tan x  cot x
cos x
Converting to Sines and Cosines
Applicable Fundamental
Trigonometric Identities
sin x
cos x
tan x 
cot x 
cos x
sin x
1
 sec x
cos x
Work Verifying Identity
1) Verify the identity cot 2 x(sec 2 x  1)  1 .
More Complicated Side of Identity
Method Used to Verify Identity
Work Verifying Identity
Applicable Fundamental
Trigonometric Identities
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
2) Verify the identity cos x  sin x tan x  sec x .
More Complicated Side of Identity
Methods Used to Verify
Identity
Applicable Fundamental
Trigonometric Identities
Work Verifying Identity
3) Verify the identity cos 2 x  sin 2 x  1  2 sin 2 x .
More Complicated Side of Identity
Method Used to Verify Identity
Work Verifying Identity
Applicable Fundamental
Trigonometric Identities
Pre-Calculus /Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Block: ______
Exit Ticket
Verifying Trigonometric Identities
Verify the identity
tan x cot x
 sec x .
cos x
Pre-Calculus/Trigonometry 3
Fall 2008
Name: ____________________________
Date: ____________
Exit Ticket
Verifying Trigonometric Identities
Verify the identity
tan x cot x
 sec x .
cos x
Block: ______