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Monica Broz
EDU 377
Unit plan outline
Unit: Trigonometric Ratios and Functions
Day 1:
Review some skills needed for new unit: using the Pythagorean Theorem, solving equations
using inverse functions, and finding angle measures in triangles. Introduce the use of
trigonometry with right triangles.
Technology used is polleverywhere.com (this is a form of an informal pre-assessment of
standards), and PowerPoint.
Differentiated instruction in the extension for those who are ready to move on and those that
need extra help.
Day 2:
Finish up any questions still on using trigonometry with right triangles (SOH CAH TOA). Then
define general angles and use radian measure.
Differentiated instruction with the mini project. Students have the chance to find their own
example in whatever interests them most. Then the extension are for those ready to move on.
Those that finish early will also be able to help others (this would be monitored).
Day 3:
(Formative assessment): A short quiz on what’s been taught thus far, after questions are
answered. (anticipating that day 1 and 2 will run over)
Day 4:
Evaluate trigonometric functions of any angle.
Technology should appeal to those visual/kinesthetic learners as they use a program on
Geogebra.
The extension includes differentiating with different learning levels.
Day 5: Evaluate inverse trigonometric functions.
Day 6:
Finish up day 5.
(Formative Assessment): Quiz on a mix of evaluating trigonometric functions and inverse
trigonometric functions.
Day 7:
Apply Law of Sines.
There is an activity today that allows the kinesthetic learners to learn more. It involves
collaboration which is great for those auditory learners and the visual learners will appreciate it
as well.
The calculators are needed or desmos.com.
Day 8:
Apply Law of Sines.
Extension allows for differentiated instruction with different learning levels.
Real world project is differentiated instruction for different interests and different learning
modalities.
Calculators are needed or desmos.com.
Day 9:
Apply Law of Cosines.
Mini project which is part of differentiated instruction with interests.
Calculators are needed or desmos.com.
Day 10:
(Formative Assessment): Quiz on law of sines and law of cosines.
Day 11: A mix review on everything from the unit.
Day 12: Test over the unit.
Standards to use
Domain: Trigonometric Functions HS.F-TF
Cluster: Extend the domain of trigonometric functions using the unit circle.
Code Standards Annotation
HS.FTF.1
Understand that the radian measure of an angle is the length of the arc on the unit circle
subtended by the angle. ↑Comment: This standard assumes that all students know and understand
that there are approximately 6.28 radius lengths around the circumference of any circle.
Radians are the preferred unit of measure. There should be a natural connection
from students’ previous knowledge of circumference to radian measure.(ND)
HS.FTF.2
Explain how the unit circle in the coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian measures of
angles traversed counterclockwise around the unit circle.
↑Comment: The following pre-requisite skills must be mastered: right triangle
trigonometry and knowledge of radian measure. (ND)
HS.FTF.3
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π /3,
π/4 and π/6, and use the unit circle to express the values of sine, cosine,
and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any
real number.
HS.FTF.4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric
functions.
Model periodic phenomena with trigonometric functions.
Code Standards Annotation
HS.FTF.5*
Choose trigonometric functions to model periodic phenomena with specified amplitude,
frequency, and midline. ↑Comment: In an effort to model periodic phenomena students must
have mastery of the following pre-requisite skills: knowledge of the characteristics of
trigonometric graphs and effects of their transformations on an equation.
Example: The depth of the ocean at a swim buoy reaches a maximum of 6 feet at 3
A.M. and a minimum of 2 feet at 9:00 A.M. Write a trigonometric function that
models the water depth y (in feet) as a function of the time t (in hours). Assume
that t=0 represents 12:00 A.M.
HS.FTF.6
(+) Understand that restricting a trigonometric function to a domain on which it is always
increasing or always decreasing allows its inverse to be constructed.
HS.FTF.7*
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts;
evaluate the solutions using technology, and interpret them in terms of
the context.
Cluster: Prove and apply trigonometric identities.
Code Standards Annotation
HS.FTF.8
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.
Students might “prove” by providing a formal proof, demonstrating, or justifying.
See the glossary for a definition of mathematical proof. (ND)
Example:
Given θ is a Quadrant II angle and sin θ = 4/5, find cos θ using the Pythagorean
Identity.