4C.FTF.9.12.8.11
2011
Domain: Functions
Cluster: Prove and Apply Trigonometric Identities
Standards:
9(+). Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Essential Questions
Enduring Understandings




What approaches can
be used to verify an
identity?
How can trigonometric
expression be used to
solve real-world
problems?
How do you prove
trigonometric
identities?
Content Statements


Students will use sum
a difference formulas
to evaluate
trigonometric
functions and verify
identities.
Students will rewrite
trigonometric
expressions is
different forms to help
solve problems.
Assessments



You can use identities to
rewrite trigonometric
expressions.
Identities are used to
evaluate, simplify, and solve
trigonometric expressions.
Formulas can be applied to
solve real-world problems.
Identities can be used to
analyze a harmonic motion
equation.
Activities, Investigation, and Student Experiences
Find the exact value of the expression.
5

5
 cos sin
12
12
12
12

11

11
 sin sin
2. cos cos
12
12
12
12
1. sin

cos
Find the value of the expression in terms of sin x and cos x .
 3

a ) sin 
 x
 4

b) cosx   


c) cos x  
3

 5

d ) sin 
 x
 6

Prove that:
1. (sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 =
tan(θ)cot(θ)
4C.FTF.9.12.8.11
Verify the identity
2


1. cos  x  
(cos x  sin x)
2
4

2
 3

2. cos
 x  
(cos x  sin x)
2
 4

2


3. sin   x  
(cos x  sin x)
2
4

Prove that:
1. sin x cos x tan x = 1 − cos2 x
2. tan x + cot x = sec x csc x
3. sec t cot t = csc t
4.
Find the exaclt value of th expressions.
1. cos
2. sin

12

12
cos
cos
11

11
 sin sin
12
12
12

3
 cos

12
sin

3
2011
4C.FTF.9.12.8.11
Equipment Needed:
Calculators (graphing)
Smart board
White board
Overhead
2011
Teacher Resources:
http://us.attanolearn.com/excel/high-school-mathstrigonometric-functions-sum-difference-identities-cosine.jsf
http://www.cramster.com/definitions/angle-sum-anddifference/938
http://www.algebralab.org/lessons/lesson.aspx?file=Trigono
metry_TrigSumDifference.xml
http://www.mathematics24.com/trigonometry/15-SumDifference-and-other-Trig-Formulas.html