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A+LSCURRICULUM
GUIDE
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Mathematics - Trigonometry
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Grade Levels
11-12
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The A+LS Mathematics
curriculum is a comprehensive, completely integrated curriculum for grade
levels 1-12. A sequence of 18 titles provides an extensive, integrated
solution that is fully correlated to major mastery standards and leading,
adopted textbooks.
In addition to a complete mathematical
curriculum that is appropriate at each grade level, each title contains
exercises that require the student to choose operations and develop strategies
to solve problems. Students learn to use common sense, mental math, estimation,
and other methods to solve problems and check answers for reasonableness.
The Mathematics titles develop knowledge
of mathematics skills and their use in practical situations by utilizing
a four-step approach: Study, Practice, Test, and Essay modules are
used to define the instructional environment. The Study module provides
a text- and graphics-based delivery of material that is reinforced by pictures
and diagrams supported by a wealth of content. All graphics magnify to
full screen size to concisely present and reinforce these concepts. The
Practice
module provides the students, in a non-scored and non-graded environment,
to practice skills acquired through studying. Engaging, interactive feedback
prompts the student to right answers when wrong answers to questions are
entered. The student has instant access to the study material for reference.
In the Test module, the student takes a scored examination, the
results of which are recorded in the A+LS Management System.
Upon completion of the Test, the student electronically "turns in"
the test and may instantly see test results and correct answers to questions
missed. The Essay module allows the student to compose individual,
free-form answers to a wide variety of questions and problems.
| LESSON
# |
LESSON
TITLE |
LESSON
CONTENT |
|
1
|
Angles |
Angles,
angle terminology, radians, reference angles |
|
2
|
Sine
Cosine and Tangent |
The
unit circle, finding values from endpoint, defintion of sine, cosine, and
tangent |
|
3
|
Values
of Sin Cos and Tan |
Values
of sine, cosine, and tangent of various angles, using the calculator to
find values |
|
4
|
Reciprocal
Functions |
Definition
and value of secant, cosecant, and cotangent |
|
5
|
The
Pythagorean Theorem |
The
Pythagorean Theorem; calculating sides of right triangles |
|
6
|
Review
1 |
|
|
7
|
Inverse
Functions |
Definition
and value of inverse trig functions |
|
8
|
Solving
Right Triangles |
Using
trig functions and the Pythagorean Theorem to solve right triangles |
|
9
|
Trigonometry
Applications |
Using
trig to solve real world problems |
|
10
|
Law
of Sines 1 |
Definition
of law of sines and applicatiosns |
|
11
|
Law
of Sines 2 |
Further
application of the Law of Sines; determining the number of triangles, and
solving triangles |
|
12
|
Law
of Cosines |
Definition
of law of cosines and solving triangles |
|
13
|
Solving
Triangles |
Using
trig functions and the Laws of Sines and Cosines to solve triangles |
|
14
|
Triangle
Applications |
Solving
triangles in word problems |
|
15
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Areas
of Triangles |
Formulas
for area of triangles |
|
16
|
Review
2 |
|
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17
|
Trigonometric
Identities |
Definition
of identity, reciprocal identities, quotient identities, Pythagorean identities,
symmetry identities |
|
18
|
Verifying
Trig Identities |
Verifying
trigonometric identities and manipulating identities for verification |
|
19
|
Sum
Difference Identities |
Sum
and difference for sine, cosine, and tangent; using cofunction identities |
|
20
|
Graphing
Trig Functions 1 |
Graphs
of sine, cosine, tangent and reciprocal functions; finding values using
graphs |
|
21
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Graphing
Trig Functions 2 |
Analyzing
amplitude, period, and phase shift; graphing functions and compound functions |
|
22
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Graphing
Trig Functions 3 |
Graphs
of inverse functions; finding values using graphs |
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23
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Review
3 |
|
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24
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Double
- and Half-Angles |
Double-angle
and half-angle identities |
|
25
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Solving
Trig Equations |
Solving
equations involving trig functions; principal values, solving for principal
and all values |
|
26
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Central
Angle Application |
Applications
of central angles; arclength, linear and angular velocity, area of circular
sectors |
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27
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Simple
Harmonic Motion |
Writing
equations for simple harmonic motion; using equations for information;
frequency |
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28
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Review
4 |
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29
|
Comprehensive
Exam |
Comprehensive
exam of course content |
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