A2.F.TF.5
2011
Domain: Trigonometric Functions
Cluster: Model periodic phenomena with trigonometric functions
Standards: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Essential Questions
How to translate and reflect
trigonometric graphs?
How do we choose which
trigonometric function to
model periodic phenomena
with amplitude and
frequency?
Enduring Understandings
Trigonometric graphs model real
world situations such as wave
motion, Richter Scale,
amusement park rides, and heart
rate.
Content Statements
Recognize and graph
periodic and trigonometric
functions.
Write and graph equations
of translations of
trigonometric functions.
Assessments
The height “H” in feet above the ground of the seat of a
playground can be modeled by H(θ) - -4 cos θ + 6, where
θ is the angle that the swing makes with a vertical
extended to the ground. Graph the height of a swing’s
seat for 0° < θ < 90°. How high is the swing when θ =
60°?
Activities, Investigation, and Student Experiences
Write and graph a model using the tangent function that gives
distance “d” in feet from the top of a building as a function of
the angle of elevation.
Ex. You are standing 120 feet from the base of a 260’ building
watching your friend go down the side of the building in a glass
elevator.
Tan θ = opp/adj = (260 – d) / 120
120 tan θ = 260 – d
120 tan θ – 260 = – d
-120 tan θ + 260 = d
A2.F.TF.5
2011
What is the amplitude for y = -4 cos 3πx?
a. -4
b. 4
c. 3
d. 3π
Which is not in the domain of y = cot x?
a. –π/2
b. 0
c. π/2
d. 3π/2
Sketch the graph of a periodic function with a period of 10
and an amplitude of 5
Equipment Needed:
SMARTBOARD
GRAPHING CALCULATOR
Internet Access
Teacher Resources:
http://www.khanacademy.org/math/trigonometry/v/usingtrig-functions
http://www.khanacademy.org/math/trigonometry/v/usingtrig-functions-part-ii
http://www.khanacademy.org/science/physics/v/introduction
-to-waves