Trigonometry
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Course Description
Trigonometry, a one-semester course, prepares students for further study of
mathematical topics in calculus and physics. The course begins with a review of righttriangle trigonometry. Students then study the unit circle and the graphs of basic
trigonometric functions (sine, cosine, and tangent) and their inverses, as well as the
relationships of these functions to chords and right triangles. In addition, students apply
their study of trigonometric functions and identities to find angles of elevation and
depression and solve right triangles. The course concludes with the introduction of the
complex number plane and the polar coordinate system. Prerequisites: Algebra I,
Geometry, Algebra II
Course Objectives
When you finish this course, you will be able to:
 Solve problems involving right triangles by using the six trigonometric functions
 Convert between degrees and radians
 Find arc length using degrees and radians
 Use the definitions of the trigonometric functions and their inverses to evaluate
expressions and graph functions
 Prove trigonometric identities and simplify others by using the identity in terms of
sine
 Use the law of sines and the law of cosines and apply those laws to solve
problems
 Use the concept of vectors to model situations defined by magnitude and direction
 Perform operations involving complex numbers
 Determine the polar coordinates of a point given in rectangular coordinates and
vice versa
 Represent equations given in rectangular coordinates in terms of polar coordinates
 Represent a complex number in polar form and know how to multiply complex
numbers in their polar form
Course Assignment Values
Assignment Type
Points
Possible
12 Assignments
1 Activity
2 Graded Discussions
5 Unit Tests
1 Midterm Exam
Weight
145 pts
29%
35 pts
7%
5 pts
1%
220 pts
44%
40 pts
8%
©2011 Advanced Academics, Inc. All Rights Reserved.
Assignment Type
Points
Possible
1 Final Exam
Course Totals
Weight
60 pts
12%
510 pts
100%
Suggested Course Schedule
The suggested time frame shown below is based on learning sessions. A learning
session is a 45-minute period of time. This course should take approximately 90
learning sessions to complete, but this schedule is just a suggestion. You may work on
each unit at your own pace, completing as many learning sessions as you’d like in one
sitting. However, keep in mind that you must finish the entire course within the time
specified by your school district.
Learning
Session
1-12
13-40
Content Covered
Unit 1: Functions and Graphs
Trigonometry is used to find distances that can’t be easily measured. For
example, a surveyor may need to find the distance between two sides of
a canyon. Since the distance they are measuring is so great, it is not
feasible for them to take out a tape measure. Surveyors use right
triangles to measure that distance without having to actually measure
manually.
In this unit, you will learn the six key trigonometric ratios that allow you to
solve right triangle problems. You will then apply these ratios to solve for
unknown sides.
In this unit, there will be:
2 Assignments
30 pts
1 Unit Test
40 pts
Unit 2: The Unit Circle
In this unit, you will study the two units of measure angles, degrees and
radians. You will also learn about a very useful tool called the unit circle.
You will use the skills you learned in the previous unit to find the sine and
cosine of all of the major angles in the four quadrants. The unit circle is a
helpful tool for finding these trigonometric ratios without the use of
calculators. Finally, you will learn how to graph the three main
trigonometric functions: sine, cosine, and tangent.
In this unit, there will be:
2 Assignments
1 Activity
30 pts
35 pts
©2011 Advanced Academics, Inc. All Rights Reserved.
1 Graded Discussion
1 Unit Test
41-42
43-58
59-74
75-88
5 pts
50 pts
Trigonometry Midterm Exam
40 pts
Unit 3: Identities and Equations
This unit will help you develop an understanding of the half-angle,
double-angle, and addition formulas for sines and cosines. You will learn
to use those formulas to prove or simplify other trigonometric identities.
In this unit, there will be:
3 Assignments
25 pts
1 Graded Discussion
5 pts
1 Unit Test
40 pts
Unit 4: Applications of Trigonometry
In this unit, you will consider methods of solving oblique triangles using
the law of sines and the law of cosines. You will also use these laws and
Heron’s formula to find areas of triangles. Vectors will also be discussed
in this unit as an application of trigonometry.
In this unit, there will be:
2 Assignments
25 pts
1 Unit Test
50 pts
Unit 5: Complex Numbers and Polar Coordinates
In this unit, you will perform operations on complex numbers and explore
the trigonometric form of complex numbers. DeMoivre’s theorem and
the nth root theorem will be used to find powers and roots of complex
numbers in trigonometric form.
Until now, you have used a rectangular coordinate system to locate a
point in the coordinate plane. An alternative method is to use a polar
coordinate system, wherein a point is located by giving a distance from a
fixed point and an angle from some fixed direction. In this unit, you will
use polar coordinates to transform between polar and rectangular
coordinates and write parametric equations.
In this unit, there will be:
3 Assignments
1 Unit Test
Trigonometry Final Exam
35 pts
40 pts
60 pts
©2011 Advanced Academics, Inc. All Rights Reserved.
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information without the written permission of the student’s parent or legal guardian.
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Disability Statement
If you have a disability or condition that may affect your ability to succeed in this course,
please contact your teacher. It’s important that you discuss the problem with him or her
so accommodations may be made to give you every opportunity to perform well. Your
teacher and virtual school program coordinators are committed to helping students with
disabilities succeed, and every request will be treated with respect and confidentiality.
©2011 Advanced Academics, Inc. All Rights Reserved.