:
Campus: Princeton High School
Author(s): Ferguson, Banschbach, Folsom, Ruckman
Date Created / Revised: January 2016
Six Weeks Period: 4th
Grade Level & Course: 12th PreCalculus
Timeline: 18 days
Unit 7 Title: Problem Solving with Trigonometric Ratios
Stated Objectives:
TEK # and SE
Lesson #
P.1A apply mathematics to problems arising in everyday life, society, and the workplace
P.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a
solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
P.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques,
including mental math, estimation, and number sense as appropriate, to solve problems.
P.1D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate.
P.1E create and use representations to organize, record, and communicate mathematical ideas.
P.1F analyze mathematical relationships to connect and communicate mathematical ideas.
P.1G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral
communication.
P.2P determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world
problems.
P.4E determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical
and real-world problems.
P.4F use trigonometry in mathematical and real-world problems, including directional bearing.
P.4G use the Law of Sines in mathematical and real-world problems.
P.4H use the Law of Cosines in mathematical and real-world problems.
See Instructional Focus Document (IFD) for TEK Specificity
Key Understandings
*the students will be able to identify and correctly discuss all six trigonometric ratios in a right triangle.
*the students will be able to discuss when trigonometric ratios are needed to solve right triangles.
*the students will be able to correctly apply the Law of Sines and Law of Cosines to non-right triangles.
*the students will be able to correctly label key parts of the unit circle.
*the students will be able to use the unit circle to find exact trig values using reference angles.
*the students will be able to convert between radians and degrees and know the importance of each unit of measure.
*the students will be able to determine the arc length and sector area of a portion of a circle.
*the students will be able to sketch the graphs of trigonometric functions and describe their properties.
*the students will be able to relate the graphs of trigonometric functions to real world situations.
Misconceptions
*students may need a refresher on simplifying radicals and rationalizing denominators.
*students may draw their angles of depression incorrectly.
*students need to remember to have their calculator set to degree mode to evaluate trig values.
Key Vocabulary
Opposite, adjacent, hypotenuse, radian, degree, unit circle, elevation, depression, sine, cosine, tangent,
Materials, Resources, Notes
Suggested Day
5E Model
Instructional Procedures
Day 1 Tuesday, January
5th
Topic: Simplifying
Radicals
OBJECTIVE: We will review simplest radical form.

EXPLAIN: We will be revisiting the topic of simplifying radicals, which will be used in
the upcoming unit. We simplify radicals by finding the largest square number that
divides evenly into our radicand. Students need to be able to generate the list of
square numbers as well as know most of their roots without a calculator.

(Engage, Explore, Explain, Extend/Elaborate, Evaluate)
Projector, pencils, spirals,
paper, calculators
Teacher made WS
CLOSING TASK: I will be able to write a radical expression in simplest form.
Day 2 Wednesday,
January 6th
Topic: Rationalizing
Denominators
OBJECTIVE: We will rationalize denominators that contain radicals.

EXPLAIN: We will be revisiting the concept of rationalizing denominators, which will
be used in the upcoming unit. Expressions in simplest form contain one simplified
radical in the numerator of a fraction only. If there are radicals in the denominator, we
must get rid of them. This process is called “rationalizing”. To rationalize, multiply by
a fancy form of “1”. (Multiply the top and bottom by the radical in the numerator.)
After rationalizing the denominator, have students simplify the remaining radical (if
possible) and the leading fraction (if possible). See example below.

Projector, pencils, spirals,
paper, calculators
Teacher made WS
CLOSING TASK: Explain to a classmate how and when rationalizing a denominator
is necessary.
Day 3 Thursday, January
7th
Topic: Pythagorean
Theorem
OBJECTIVE: We will revisit the concept of Pythagorean theorem.

ENGAGE: Teacher will pose a problem that requires Pythagorean theorem to solve.
Have students discuss how to appropriately come to the correct solution.

EXPLAIN: Pythagorean Theorem is a previously taught concept. We will be
revisiting and expanding this concept as it will appear again later in the unit. Students
should be able to solve for the third side in a right triangle given the other two. We
will now focus on leaving our answers in simplest radical form. Have students
complete real-world application problems as well. Discuss when the students can
solve using subtraction or addition, depending on if the hypotenuse is given or
missing.
CLOSING TASK: What short cuts can be used when applying Pythagorean
theorem?
Projector, pencils, spirals,
paper, calculators
Teacher made WS
Day 4 Friday, January 8th
Topic: QUIZ
OBJECTIVE: We will demonstrate our knowledge of radicals and Pythagorean
theorem.


Pencils, calculators
QUIZ

Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
4.2
Possible assignment page
366 #1-8, 25-26, 29-30, 35-36
EXPLAIN: Teacher can answer a few questions or have the students complete a
short warm up before the quiz.
*ASVAB scores*
CLOSING TASK: none.
Day 5 Monday, January
11th
Topic: Right Triangle
Trigonometric Ratios (Six)
OBJECTIVE: We will introduce the six trigonometric ratios with right triangles.

EXPLAIN: We will label the sides of a right triangle according to one of the acute
angles as hypotenuse, opposite and adjacent. SOH CAH TOA can be used as a
memory tool. Discuss the reciprocal trig ratios and how their values relate. Express
ratios in simplest radical form. Students should also practice entering into the
calculator a trig expression, rounding to a specified value, for example to the nearest
thousandth. Calculator must be in degree mode.

CLOSING TASK: Explain the relationship(s), if any, of the six trigonometric ratios.
Day 6 Tuesday, January
12th
Topic: Right Triangle Trig
(Solving for a side)
OBJECTIVE: We will use trig ratios to solve for missing side lengths in a right
triangle.


EXPLAIN: We will use the trig ratios discussed yesterday to solve for missing side
lengths in a right triangle. There will be two scenarios when solving for a side length,
the variable will be in the numerator or denominator. If the variable is in the
numerator, multiply to solve for x. If the variable is in the denominator, switch the trig

Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
4.2
Possible assignment, page
367 #49-54
with the x and divide. Remind the students that their calculator must be in degree
mode, since our angles are measured in degrees.
CLOSING TASK: Explain the short cut discussed when calculating the side length.
Day 7 Wednesday,
January 13th
Topic: Right Triangle Trig
(Solving for angles)
OBJECTIVE: We will use trig ratios to solve for missing angles in a right triangle.

EXPLAIN: We will use the trig ratios discussed yesterday to solve for missing angle
measures. Calculator must be in degree mode and we will round all angles to the
nearest whole degree. Inverse trig must be used to solve for the angles.

Projector, pencils, spirals,
paper, calculators
Teacher made WS
CLOSING TASK: What function on the calculator is needed when using trig to solve
for an angle?
Day 8 Thursday, January
14th
Topic: Solving Right
Triangles
OBJECTIVE: We will use trig to solve a right triangle.

EXPLAIN: Today we will ty it all together, trig, Pythagorean theorem and the triangle
sum theorem to solve right triangle. When solving a right triangle you need to find the
measure of all the missing angles and sides. This requires the use of trig only once.
Trig can be used multiple times to determine all sides and angles if preferred.

**Presentation: Bobby
Petracelli**
CLOSING TASK: I will study my notes and assignments to prepare for tomorrow’s
quiz.

Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
4.2
Possible assignment page
367 #55-58
Day 9 Friday, January 15th
Topic: Quiz
OBJECTIVE: We will demonstrate our knowledge of right triangle trig.

EXPLAIN: Teacher can answer a few questions or have the students complete a
short warm up before the quiz.

Projector, pencils, spirals,
paper, calculators
QUIZ
CLOSING TASK: none.
Day 10 Tuesday, January
19th
Topic: Right Triangle Trig
Applications
OBJECTIVE: We will apply trigonometry to real world scenarios.

EXPLAIN: We will continue our study of right triangle trig by relating it to the real
world. Discuss angle vocabulary of elevation and depression. Both are formed by
horizontal lines and lines of sights either below or above the horizontal line. Students
need to be comfortable sketching a picture of what the word problems are describing
if no picture is given. Also, they should be able to determine which side or angle the
problem is asking them to find.




Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
4.2, EXAMPLE 6
TEXTBOOK reference section
4.8, EXAMPLE 1
Possible assignment page
367, #61-62, 64
Page 431 #1, 3-6, 8, 10-11, 16,
22
CLOSING TASK: Explain the difference between angles of elevation and depression.
Day 11 Wednesday,
January 20th
Topic: REVIEW
OBJECTIVE: We will review right triangle trigonometry.

EXPLAIN: Students will complete an in class review of right triangle trigonometry.
They may work together and will be able to check their answers and ask questions
before leaving class today.

Projector, pencils, spirals,
paper, calculators
Teacher made REVIEW & KEY
CLOSING TASK: I will study my notes and review to prepare for tomorrow’s test.
Day 12 Thursday, January
21st
Topic: Right Triangle Trig
TEST
OBJECTIVE: We will demonstrate our knowledge of right triangle trigonometry.

EXPLAIN: Teacher can answer any last minute questions, if they choose, but the
majority of the class period should be devoted to the test. Remind the students to
make sure their calculator is in DEGREE mode.

CLOSING TASK: none.
Projector, pencils, spirals,
paper, calculators
TEST
Day 13 Friday, January
22nd
Topic: Introduction to the
Law of Sines
*early release*
OBJECTIVE: We will begin Law of Sines.

EXPLAIN: Today is an early release day. We will introduce the Law of Sines and
when it can be used. The Law of Sines can be used definitively in triangles where the
information given is in the form of AAS or ASA. These are the two types we will be
focusing on through our study of Law of Sines.


Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
5.5, examples 1 & 2
Possible assignment page
484 #1-12, 25-26
CLOSING TASK: What is important about the proportions in the Law of Sines?
Day 14 Monday, January
25th
Topic: Law of Sines
continued
OBJECTIVE: We will continue our study of the Law of Sines.

EXPLAIN: This topic was introduced in the last class meeting. The teacher may
present additional examples as needed and allow the students time to complete their
Law of Sines assignment. Be sure to solve for missing angles and sides.

CLOSING TASK: Explain when you can use the Law of Sines.

Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
5.5, examples 1 & 2
Possible assignment page
484 #1-12, 25-26
Day 15 Tuesday, January
26th
Topic: Law of Cosines
OBJECTIVE: We will discuss and apply the Law of Cosines.

EXPLAIN: We will expand our discussion of using trig to solve for missing
sides/angles in non-right triangles with the Law of Cosines. The Law of Cosines can
be used when you are given a triangle with SAS or SSS information. If you are given
SSS information, you must solve for the largest angle first.


Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference section
5.6, examples 1 & 2
Possible assignment page
494, # 1-4, 5-8
CLOSING TASK: Explain when to use the Law of Sines vs the Law of Cosines.
Day 16 Wednesday,
January 27th
Topic: Law of Sines &
Cosines Applications
OBJECTIVE: We will apply the Law of Sines and Cosines to real world scenarios.

EXPLAIN: Students will need to be able to sketch a picture of various scenarios
described and then determine which Law (Sines or Cosines) is needed to determine
the solution.



Projector, pencils, spirals,
paper, calculators
TEXTBOOK reference
sections 5.5 and 5.6
Possible assignment page
485 #40, 45, 49, 51
Possible assignment page
494 #35, 38, 41, 49
CLOSING TASK: List strategies used when solving a real world application.
Day 17 Thursday, January
28th
Topic: REVIEW
OBJECTIVE: We will review the Law of Sines and Cosines.

EXPLAIN: Students will complete an in class review of trigonometry involving nonright triangles. They may work together to discuss/compare and will be able to check
their answers and ask questions before leaving class today.

Projector, pencils, spirals,
paper, calculators
Teacher made REVIEW & KEY
CLOSING TASK: I will study my review and notes to prepare for tomorrow’s test.
Day 18 Friday, January
29th
Topic: Law of Sines &
Cosines TEST
OBJECTIVE: We will demonstrate our knowledge of the Law of Sines and Cosines.

EXPLAIN: Teacher can answer any last minute questions, if they choose, but the
majority of the class period should be devoted to the test. Remind the students to
make sure their calculator is in DEGREE mode.

CLOSING TASK: none.
Accommodations
for Special
Populations
Accommodations for instruction will be provided as stated on each student’s (IEP)
Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.
Projector, pencils, spirals,
paper, calculators
TEST