©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG- November 13th – December 20th (25 days; 2 days for 6 weeks review/test; 4 days for final exams)
Major Concept #1: Trigonometric Identities
Overarching
Idea
Teacher
Guiding
Questions
241
275
241
Attributes of
Functions
How can trigonometric identities be used to simplify expressions and solve equations?

What are the sum/difference, product/sum and double/half-angle trigonometric identities?

How are the identities used to solve real world problems?
TEKS
Knowledge & Skill
The student interprets the
meaning of the symbolic
representations of
functions and operations
on functions to solve
meaningful problems. (P.2)
Equations, Functions, and
Function Models
240A

The student uses functions
and their properties, tools
and technology, to model
and solve meaningful
problems. (P.3)
Attributes
of
Functions
275
Matrix
Strand
15 DAYS
Trigonometry has practical applications in navigation, surveying, and building as well as numerous other scientific fields.
(P.2)
Equations,
Functions, and
Function Models
Matrix
#
Pre-Calculus
(P.3)
Student Expectation
Investigate identities
graphically and verify
them symbolically,
including logarithmic
properties, trigonometric
identities, and exponential
properties. (P.2C)
Use functions such as
logarithmic, exponential,
trigonometric, polynomial,
etc. to model real-life data.
(P.3B)
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. (P.3E)
TAKS
OBJ
Resource
LH
(Section 5.1)
Using
Fundamental
Identities
Time/
Pace
3 days
(P.2C)
(P.3E)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
LH
(Section 5.2)
Verifying
Trigonometric
Identities
3 days
includes
days for
review
and/or
test
Teacher Tools
Vocabulary: fundamental trigonometric
identities, reciprocal identities, cofunction
identities, quotient identities, even/odd
identities, Pythagorean identities
Teacher notes: Animated Precalculus video
tutorials for this chapter can be accessed at
http://college.hmco.com/mathematics/larson/pre
calculus_limits/1e2/ins_resources/ap.html.
Use the following login information:
Username: larpclim1e
Password: sequence
The “Study the Concept” video explains how the
quotient identities and Pythagorean identities
are derived. Students may review these videos
at any time if they have access to the Internet.
Vocabulary: conditional equation, identity
Teacher notes: In this section, students learn
how to distinguish between a conditional
equation and a trigonometric identity. Challenge
students to find at least one instance for which
the equation is not true therefore it cannot be an
identity. This is an essential prerequisite to
solving equations using trigonometric identities.
The Student Notetaking Guide will help students
organize their work and develop their strategies.
Pre-Calculus Page 1 of 3
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG- November 13th – December 20th (25 days; 2 days for 6 weeks review/test; 4 days for final exams)
Major Concept #1: Trigonometric Identities (Continued)
Overarching
Idea
Teacher
Guiding
Questions
275
275
241
Attributes
of
Functions
Equations,
Functions, and
Function Models
How can trigonometric identities be used to simplify expressions and solve equations?

What are the sum/difference, product/sum and double/half-angle trigonometric identities?

How are the identities used to solve real world problems?
TEKS
Knowledge & Skill
(P.2)
(P.3)
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
(P.2C)
(P.3E)
Attributes of
Functions
241

(P.2)
(P.2C)
Attributes
of
Functions
275
Matrix
Strand
15 DAYS (Continued)
Trigonometry has practical applications in navigation, surveying, and building as well as numerous other scientific fields.
(P.2)
(P.2C)
Equations,
Functions,
and Function
Models
Matrix
#
Pre-Calculus
(P.3)
(P.3E)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
LH
(Section 5.3)
Solving
Trigonometric
Equations
3 days
LH
(Section 5.4)
Sum and
Difference
Formulas
3 days
LH
(Section 5.5)
Multiple-Angle
and Product-toSum Formula
3 days
includes
days for
review
and/or
test
Teacher Tools
Vocabulary: general solution, quadratic type,
and extraneous solution
Teacher Notes: The Student Notetaking
Guide includes sentence starters for students
to identify the important concepts related to
solving trigonometric equations of different
types including using inverse trigonometric
functions to solve trigonometric equations.
There are also Powerpoint presentations for
each section that can be downloaded and
customized to fit your needs at
http://college.hmco.com/mathematics/larson/p
recalculus_limits/1e/assets/instructors/protect
ed/dl/solve_trig_equations.ppt.
Vocabulary: sum and difference formula,
reduction formula
Animated Precalculus videos are available for
both concepts included in this section at the
previous link in the tools for Section 5.1
above.
Vocabulary: double-angle formulas, functions
of multiple angles, squares of trigonometric
functions, functions of half-angles, products of
trigonometric functions
The online resources for this section does not
include a Powerpoint presentation, but video
lessons are available at the same link as in
the tools for Section 5.1 above.
The Chapter project aligns with Example 12
on page 414 and could be used as a studentcentered class activity.
Pre-Calculus Page 2 of 3
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG- November 13th – December 20th (25 days; 2 days for 6 weeks review/test; 4 days for final exams)
Major Concept #2: Laws of Sines and Cosines
Overarching
Idea
Teacher
Guiding
Questions
241
Matrix
Strand
Equations, Functions, and Function
Models
Matrix
#
Pre-Calculus
DAYS
The Law of Sines and the Law of Cosines are useful in determining missing lengths or angles of any triangle to solve problems
involving distance and direction.

How do you use the Law of Sines or the Law of Cosines to find dimensions or angles of any oblique triangle?

What are the similarities and differences between the Law of Sines and the Law of Cosines?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
LH
(Section 6.1)
Law of Sines
(P.3)
(P.3E)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
LH
(Section 6.2)
Law of Cosines
Time/
Pace
Teacher Tools
4 days
includes
days for
review
and/or
test
Vocabulary: Law of Cosines, Law of Sines,
oblique triangle
Teacher Notes: Geometry teachers spend a
significant amount of instructional time in
Geometry investigating triangle congruency.
Access students’ prior knowledge by
brainstorming everything students know
about relationships between sides and
angles of triangles.
Questions: What do you notice about the
triangle measurements needed to apply the
Law of Sines? How does this relate to your
previous study of triangles?
Why are the relationships between the ratios
of the sides and angles important?
Pre-Calculus Page 3 of 3
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I