Download Unit 13

Department: Mathematics
Course: AAT-H
Standards:
Common Core State Standards Unit 13: Chapter 7
Extend the domain of trigonometric functions using the unit circle
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle
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
Model periodic phenomena with trigonometric functions
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and
midline
Prove and apply trigonometric identities
Prove the Pythagorean identity and use it to calculate trigonometric ratios
Stage 1: Desired Results
Understandings
We commonly think of Trigonometry as the study of measurements in a triangle, but it's use extends to the
applications of trigonometric relationships as functions of real numbers which can be applied to a vast number
of physical phenomena involving rotations and vibrations. The trigonometric functions can be used to solve
for lengths and angle measures in triangles, even in real-life situations.
Essential Questions
How can you convert between radians and
degrees?
Knowledge & Skill
See handout attached
How can we use the trigonometry identities
to solve for missing information?
Where might you use trigonometry in reallife settings?
Stage 2: Assessment Evidence
In-class problems, verbal response, homework assignments, Problems of the Week, clean-up days for selfassessment, observation, quizzes, test
Performance Task Summary
Homework assignments
Problems of the Week
Quizzes
Test
Rubric Titles
Problems of the Week
Wrapping Function Values Quiz
Trigonometric Values Quiz
Trigonometry Unit A Exam
Self-assessment of objectives
Review of lessons
Homework corrections
Problem of the Week corrections
Partner/Group checks
Quiz corrections
Other Evidence, Summarized
Other assessment information will be obtained through
observations, classroom participation, class discussions, and
partner/group interactions. The unit assessment will be
graded, gathered, and analyzed district wide.
Stage 3: Learning Activities
In-class problems
Group activities
Board work
Class discussion
Using the graphing calculator
Unit 13: Chapter 7 Knowledge and Skills
Objectives
I can…
 Describe an angle and convert between radian and degree measures
 Evaluate trigonometric functions of any angle
 Use the fundamental trigonometric identities
 Sketch the graphs of trigonometric functions
 Sketch translations of sine and cosine function graphs
 Evaluate the inverse trigonometric functions
 Evaluate compositions of trigonometric functions
 Use fundamental trigonometric identities to evaluate trigonometric functions and simplify trigonometric
expressions
 Verify trigonometric identities
 Use standard algebraic techniques and inverse trigonometric functions to solve trigonometric equations
 Use sum and difference formulas, multiple-angle formulas, power-reducing formulas, half angle
formulas, and product-to-sum formulas to rewrite and evaluate trigonometric functions
Vocabulary
Trigonometry
Initial side
Terminal side
Standard position
Positive angles
Negative angles
Coterminal angles
Degree
Radian
Linear speed
Angular speed
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
Reference angle
Period
Amplitude
Phase shift
Damping factor
Inverse sine
Inverse cosine
Inverse tangent
Angle of elevation
Angle of depression
Bearings
Simple harmonic motion
Sum and difference formulas
Reduction formulas
Power-reducing formulas
Half-angle formulas
Sum-to-product formulas