Download A2.F.TF.8.12.08.11a

A2.F.TF.8
2011
Domain: Trigonometric Functions
Cluster: Prove and apply trigonometric identities
Standards: Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ),
or tan(θ) and the quadrant of the angle.
Essential Questions
What is a trigonometric
identity?
Why are some identities
called trigonometric
identities?
Content Statements
Graph trigonometric
functions.
Enduring Understandings
Establish a link between the
different forms of the
Pythagorean Theorem
Geometry: a2 + b2 = c2
Algebra 2: a2 + b2 = c2
Unit circle: x2 + y2 = r2
Identity: sin2(θ) + cos2(θ) = 1
Verify trigonometric
identities.
Apply/model trigonometric
identities to real life
situations.
Assessments
Rewrite each expression in terms of a single trigonometric
function
a. tan θ cot θ
Answer: 1
b.
Answer: 1/sin θ
sin 
1  cos 2 
Activities, Investigation, and Student Experiences
Given that sin θ = 4/5 and π/2 < θ < π, find the values of the five
remaining trigonometric functions of θ.
 Simplify the expression tan (π/2 – θ)sin θ
sec2   1
 Verify the identity
 sin 2 
2
sec 
 The length of a shadow is given by the formula
h sin(90   )
s
sin 
o Simplify this expression
Use the Pythagorean identity sin2 θ + cos2 θ = 1 to derive the
other Pythagorean identities, 1 + tan2 θ = sec2 θ and 1 + cot2 θ =
csc2 θ
A2.F.TF.8
Which expression is equivalent to sec θ sin θ?
a. sin θ
b. cos θ
c. csc θ
d. tan θ **
Verify the trigonometric identity
sec   1
2
sec 
2
 sin 
2
Answer
sec 
2
sec 
2

1
sec 
 1 
1 

 sec  
1  cos 2 
sin 2 
2
2
Equipment Needed:
Teacher Resources:
http://www.khanacademy.org/video/trigonometricidentities?playlist=Trigonometry
2011
A2.F.TF.8
Holt McDougal, Algebra 2, (2012)
2011