Course: Pre-Calculus
Concept (Big Idea): Trigonometry
Enduring Understanding: Trigonometry can be used to
determine indirect measurements of lengths and angles
to solve a variety of problems
Concept Pacing:
Essential Questions:
How do trigonometric and circular functions model real-world problems and their solutions?
What is the purpose for trig identities?
How is the law of sines used?
Can we do without the law of cosines?
What is the difference in solving a right triangle and any triangle?
Why do we need more identities?
Why must we know what the trig equation is asking to know the number of solutions?
Unit 1: Trig identities, Formula, and solving Trig Equations
Vocabulary (if applicable): identity, Law of Sines, Law of Cosines, Area of a triangle, Heron’s Formula (SAS), radian
Resources (if applicable): LH: 6.1, 6.2, 5.1, 5.2, 5.3, 5.4, 5.5
Arc 1 (if applicable): Area of a triangle, right triangle trigonometry, oblique triangles
Resources(if applicable):
Matrix
#
275
241
2010 – 2011
Austin ISD Curriculum Road Map
3rd Six Weeks – Nov. 9 through Dec. 16 (25 of days)
Established Goals
TEKS Knowledge & Skill
P.2: The student interprets
the meaning of the symbolic
representations of functions
and operations on functions
to solve meaningful problems
P.3: The student uses
functions and their
properties, tools and
technology, to model and
solve meaningful problems
Established Goals
TEKS Student Expectation
P.2C: Investigate identities
graphically and verify them
symbolically, including logarithmic
properties, trigonometric identities,
and exponential properties
P.3E: Solve problems from
physical situations using
trigonometry, including the use of
Law of Sines, Law of Cosines, and
area formulas and incorporate
radian measure where needed.
Unit Pacing: 15 days
Arc Pacing:
Students Will Know…
Students will be able to….
Angle measures can be expressed
in degrees or in radians
Sum and Difference Identities
Double and half-angle identities
Product and sum identities
Trigonometric Applications
Law of Sines
Law of Cosines
Area of triangles
Solving triangles
Solving trig equations
Find exact values, using the sum and
difference identities
Find exact values, using the double and
half-angle identities
Recognize the product and sum identities
Find the area of any triangle
Solve any triangle
Find the area of shaded regions
Identify the ambiguous case, using the
Law of Cosines
Solve trig equations, both with exact
values and approximate values
Student Work Products/Assessment Evidence
Other Evidence (i.e. unit tests, open ended exams,
quiz, essay, student work samples, observations, etc.)
Performance Tasks
Use the fundamental trigonometric identities to simplify trigonometric expressions, evaluate
trigonometric functions, solve trigonometric equations, and develop additional trigonometric
identities.
Use the Law of Sines & Law of Cosines to find unknown angles and side lengths Recognize
situations in which the ambiguous case SSA produces no solution, one solution, or two solutions.
Find the area of any triangle
© 2010 Austin Independent School District
Discussions, worksheets, Problems from book, Tests &
quizzes
Course: Pre-Calculus Page 1 of 4
updated 11/15/10
Course: Pre-Calculus
Lesson/Activity/
Module Name
Teacher
Resource
Student Resource
Fundamental
Identities (LH:
5.1 – 5.2)
Learning Plan
Technology (Media,
website, etc.)
http://tutorial.math.lama
r.edu/Classes/CalcI/Tri
gEquations.aspx
http://library.thinkquest.
org/C005245/ Calculator Programs
Solving Trig
Equations
(LH: 5.3)
Lecture from LH:
5.3
2010 – 2011
Austin ISD Curriculum Road Map
3rd Six Weeks – Nov. 9 through Dec. 16 (25 of days)
Other
(Include Pre-Teach Suggestions,
Intervention Suggestions,
Anchors of Support - all as links)
Review page for Pythagorean
Trig
Assessment
(Prep for Assessment,
TAKS Stems links)
Finger Trick to evaluate trig
equations
Warm Up – Verifying Identities
Exit – Solve Trig
Equations
Graphic Organizer – How to
Solve a trig equations
Jeopardy – Trig
Review
Solving Trig Equations
Trig Formulas
(LH: 5.4 – 5.5)
Law of Sines &
Law of Cosines
(LH: 6.1 – 6.2)
Lecture from LH:
5.4 – 5.5
Lecture from LH:
6.1
Notes 1 – Law of
Sines
Notes 2 – Law of
Sines (ambiguous
Case)
Warm Up – P. 406 – 97 – 104
Quiz – Trig identities &
Solving Trig Equations
Exit – Formulas
Formulas Cheat Sheet
Quiz – Exact Values
Student Practice – P. 404–406
2,5 , 7, 11, 15, 19, 23-27, off,
33–39 odd
Test Review
Test - Formulas
Student Practice 2 – p. 415–
418 1, 3, 7, 11-15 odd, 19, 20,
23–27 odd, 31–37, 41, 47-51
Notes – Law of Sines
Exit
Notes – Law of Cosines
LOC, LOS Review
Ambiguous case GSP Activity
Quiz – Solving
triangles
LOC, LOS Word Problem
examples
LOS toothpick Activity
Notes 3 – Law of
Sines (special
Case)
Solving Triangle examples
© 2010 Austin Independent School District
Course: Pre-Calculus Page 2 of 4
updated 11/15/10
Course: Pre-Calculus
Notes 4 – Law of
Cosines
2010 – 2011
Austin ISD Curriculum Road Map
3rd Six Weeks – Nov. 9 through Dec. 16 (25 of days)
Solve the Triangle
Area of a triangle
Trig Story Problems
Oil Refinery Problem
Student Practice p. 437 # 35- 42
Concept (Big Idea): Trigonometric Functions
Enduring Understanding:
The characteristics of trigonometric and circular
functions and their representations are useful in
solving real-world problems.
Concept Pacing:
Essential Questions:
How are the six trigonometric and circular functions related to each other?
How do trigonometric and circular functions model real-world problems and their solutions?
How can trigonometric graphs be used to solve trigonometric equations?
How do you determine the period of a trigonometric function?
Unit 2: Trigonometric functions & their graphs
Unit Pacing: 5 days
Vocabulary (if applicable): amplitude, angular displacement, angular velocity, circular function, cotangent, cosecant, coterminal, frequency, initial side of an
angle, linear velocity, period, phase shift, radian, secant, simple harmonic motion, sinusoidal function, standard position, terminal side of an angle
Resources (if applicable): LH: 6.1, 6.2, 5.1, 5.2, 5.3, 5.4, 5.5
Arc 1 (if applicable): Area of a triangle, right triangle trigonometry, oblique triangles
Arc Pacing:
Resources(if applicable):
Matrix
#
260
Established Goals
TEKS Knowledge & Skill
P.1: The student defines functions,
describes the characteristics of
functions, and translates among
verbal, numerical, graphical, and
symbolic representations of
functions, including polynomial,
rational, power, exponential,
logarithmic, trigonometric, and
piecewise-defined functions
Established Goals
TEKS Student Expectation
P.1B: determine the domain
and range of functions using
graphs, tables, and symbols.
Students Will Know…
Students will be able to….
Trigonometric functions have
unique and recognizable graphs.
Trigonometric functions can be
used to model real world situations
such as amplitude and frequency
of sound waves and the movement
of pendulums and Ferris wheels.
Trigonometric functions are
periodic
Sketch the 3 trig functions
Use the 3 trig functions to graph other trig
graphs that have changes in amplitude,
period, phase shift, and vertical shift
Given graphs of trig function, write their
equations
Using calculators, sketch graphs of any trig
function or combination of trig functions
involving sine, cosine, and tangent
Student Work Products/Assessment Evidence
Performance Tasks
Understand the characteristics of basic trig functions
Sketch the graphs of the trig functions
© 2010 Austin Independent School District
Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student work samples,
observations, etc.)
Discussions, worksheets, Problems from book, Tests & quizzes
Course: Pre-Calculus Page 3 of 4
updated 11/15/10
Course: Pre-Calculus
Lesson/Activity/
Module Name
Teacher
Resource
Student Resource
Graphs of Sine
and Cosine
Functions
(LH: 4.5)
Lecture from LH:
4.5
GSP Activity Radians and angles
Notes – Sine
function graph
Notes – Cosine
Function graph
2010 – 2011
Austin ISD Curriculum Road Map
3rd Six Weeks – Nov. 9 through Dec. 16 (25 of days)
Learning Plan
Technology (Media, website, etc.)
Other
(Include Pre-Teach
Suggestions, Intervention
Suggestions, Anchors of
Support - all as links)
Assessment
(Prep for
Assessment, TAKS
Stems links)
Exit
GSP Activity Sine & Cosine
http://education.ti.com/html/t3_free
_courses/calculus84_online/index.
html
Student Practice - Graphing Sine &
Cosine
http://archives.math.utk.edu/visual.
calculus/0/index.html
Quiz – Solving
triangles
Notes – Sine & Cosine
http://www.algebasics.com/
Sine Curve Equation
A slinky graph – CBR activity
http://www.themathpage.com/atrig/
graphs-trig.htm#period
LOC, LOS Review
Periodic Regression
Measuring Mountains Regression
Let the Sun Shine Regression
Sine Regression
Temperature Regression
Graphs of other
Trig Functions
(LH: 4.6)
Notes – Tangent
Function graph
Graphing Trig Functions
Test Review
Tangent GSP Activity
Test
Tangent Function
Cumulative Review
Review Trig Functions GSP Activity
© 2010 Austin Independent School District
Course: Pre-Calculus Page 4 of 4
updated 11/15/10