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What You Should Already Know

Before beginning this course you should have taken ALG 057 and GEOM 043 or the equivalent of a full year of algebra II and a full year of geometry.

Learning Outcomes

You will be expected to demonstrate mastery of the following outcomes throughout your study in this course:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

You should keep these eight primary outcomes in mind as you complete this course or any math course. This course’s specific outcomes will help you to expand on mathematical principles you learned in previous math classes. After successful completion of the course you will be able to do the following:

  1. Define the sine, cosine, tangent, cotangent, secant, and cosecant functions.
  2. Determine the difference between degree and radian angle measures.
  3. Compute the values obtained by the trigonometric functions at integral multiples of π/6 and π/4 (30° and 45°).
  4. Using a calculator, calculate the value obtained for trigonometric functions of any degree or radian measure.
  5. Solve trigonometric equations.
  6. Relate the values of trigonometric functions of acute angles with those of larger angles.
  7. Graph trigonometric functions and transform them vertically, horizontally, and by stretching.
  8. Determine the difference between a relation and a function and apply the properties of graphing.
  9. Define the inverse trigonometric functions.
  10. Prove selected trigonometric identities, including reciprocal, ratio, Pythagorean, sum, difference, double-angle, and half-angle identities.
  11. Find measures of triangles using the law of sines and cosines and determine the area of a triangle using trigonometry.
  12. Use trigonometry to perform vector calculations including magnitude, direction, addition, subtractions, scale values, and use the dot product to calculate the angle between two vectors.
  13. Convert a complex number to trigonometric form and convert from trigonometric form to a complex number.
  14. Plot points using polar coordinates. Convert between polar and Cartesian coordinates.

Course Materials

There is no textbook for this course; the course content is all you will need. You will also need a scientific calculator; a graphing calculator will not be necessary for this course, but it may be wise to invest in one for future math courses.

Internet Access

This course's explorations require an internet connection capable of delivering streamed audio and video through Adobe Connect.

Test your connection: Adobe Connection test

It is necessary to have a headset or speakers connected to your computer to hear the exploration and a microphone to vocally participate. A webcam is not necessary for active participation.

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Course Organization

Each lesson is broken into sections based on learning outcomes. Each section has content for you to learn and is followed by small, non-graded Self Check that will help you determine how well you are learning the material.


Unit Quizzes and Review Quizzes

You’ll complete a unit quiz at the end of each unit. There are also three cumulative review assignments covering all of the concepts from the preceding units. These assignments are open-book quizzes. If you find that you are relying heavily on the course material to successfully complete these assignments, you will want to increase your study time because the final exam is not open book.

Show Your Work Assignments

You will be required to show your work or justify your answers during Show-Your-Work assignments and on the exam. Your work will be reviewed for partial credit, and your grade will be updated when applicable. For partial credit, you must show your work in the space provided. The following rubric shows how your work will be graded:

Full credit Answer is correct; clear understanding of mathematical processes and reasoning is demonstrated.
3/4 credit Answer is incorrect; clear understanding of mathematical processes and reasoning is demonstrated, but with one or two minor errors.
Half credit Answer is incorrect; multiple minor errors; demonstrates incomplete understanding of topic.
1/4 credit Answer is incorrect; critical errors; demonstrates incomplete understanding of topic.
No credit Answer is incorrect; no work or justification is shown, or the work demonstrates lack of understanding of topic.

Essay Assignments

At midcourse and at the end of your course, you will complete an essay assignment. In these assignments, you will be required to describe your strategies and reasoning for various mathematical principles. Please note that providing correct answers is not the goal of the essay assignments; your ideas and reasoning are much more important (notice how providing correct answers only accounts for one quarter of the possible credit). Please take the time to explain your thought process and steps for solving the problems. Here’s how your work will be graded:

Full credit Response employs correct principles and explains how solution was derived; correct strategies used.
3/4 credit Response employs correct principles with minor flaws; response partially explains how solution was derived; correct strategies used but with one or two minor errors.
Half credit Response employs principles with moderate flaws; response partially explains how solution was derived; incorrect strategies used.
1/4 credit Response may display correct answers with little or no explanation; response employs principles with critical flaws or doesn’t explain how solution was derived; incorrect strategies used.
No credit No explanation is shown or the work demonstrates lack of understanding of correct strategies; answers are incorrect.

Explorations and Orientation

This course includes exploration activities in select lessons. An exploration is a chance for you to interact with your teacher, TA(s), and other students in the course about specific topics. Each exploration is worth an equal amount, and all the explorations together account for 20% of your final grade. You must complete each exploration before you can take any later graded assignments. There are two types of explorations in this course, Discussion Board type, and Live Online meeting type.

Check the course policies for specifics of these activites.

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After completing all units, you will take the final exam. As noted, the final exam is comprehensive—in other words, it covers all material in this course. It consists of around 60 questions, which are very much like those in the unit quizzes. You may use a scientific or graphing calculator on the exam. You will be required to show your work for some exam questions.

It is a closed-book exam, but you will be allowed to bring a page of hand-written notes. This page should be an 8½" × 11" (or A4) size, and you may only write on one side. For more information, see the Final Exam Preparation section after the last lesson.

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Other Resources

There is a course discussion board at the end of the course, as well as a course wiki. The discussion board is designed for students to connect, discuss course-related matters, and share ideas with each other. The wiki is designed for the instructor or students to post information that may provide enrichment or relevant information for the course to the students.


The following tables show the grading breakdown and grading scale for this course:

Graded Event Weight Quantity Total
Unit Quizzes 2% 12 24%
Show Your Work 2% 12 24%
Review Quizzes 1% 3 3%
Show-Your-Work Review 1% 3 3%
Essay Assignments 8% 2 16%
Explorations 5% 4 20%
Final Exam 10% 1 10%

Grading Scale
A 100%–93%
A− 92%–90%
B+ 89%–87%
B 86%–83%
B− 82%–80%
C+ 79%–77%
C 76%–73%
C− 72%–70%
D+ 69%–67%
D 66%–63%
D− 62%–60%
E (fail) 59% or below

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Inappropriate Use of Course Content

All course materials (e.g., outlines, handouts, syllabi, exams, quizzes, media, lecture content, audio and video recordings, etc.) are proprietary. Students are prohibited from posting or selling any such course materials without the express written permission of BYU Independent Study. To do so is a violation of the Brigham Young University Honor Code.

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Course Policies

These policies are specific to this course. For additional information about general policies, please refer to Independent Study Course Policies page.

Unit Quizzes

Summary: 15 computer-graded assignments, may be resubmitted as often as you like.

Show Your Work Assignments

15 teacher-graded short answer assignments, may be resubmitted once

Essay Assignments

2 teacher-graded essay assignments, may be resubmitted once

Explorations and Orientation

Summary: and 4 explorations, (see descriptions for resumission details)

Discussion Board Explorations

Explorations involving discussion boards consist of three parts:

  1. A graded exploration assignment. This assignment requires you to apply the skills you have learned to a relevant problem and submit it for grading.
  2. A graded discussion of the exploration’s ideas. After you have submitted your exploration assignment, you will join other students and your teacher and/or TA in a discussion of concepts from the exploration in a discussion-board format. You'll be required to post your answers from the exploration assignment into the discussion board. Half the points from this assignment are awarded when you post your work, and you earn the other half of your points by critiquing the work of other students. You may keep posting until you achieve the grade you want. See the rubric below for details.
  3. A summary of the big idea behind the exploration. This section will contain a summary of the exploration and will aid you as a review tool. This section is not graded.

The following rubric governs how your exploration work will be graded:

10 pointsYou will automatically be awarded 10 points when you submit your exploration assignment. Your grader will review this work and may take points off for missing information or for incomplete work.
10 pointsYou will earn 10 points when you post the work from your exploration assignment into the discussion board for other students to critique.
10 pointsUp to 5 points per post, with a maximum of 10 points, will be awarded for critiquing the work of other students or responding productively to any instructionally related post in the discussion board. Each post will be evaluated by a grader who will award up to 5 points per post for your work in helping clarify, correct, and/or critique the work from any post in the discussion board, including your own. You may continue to post to the discussion board until you have earned the number of points you wish, and even after.
Total30 points are possible for discussion board explorations.

Live Online Explorations

Explorations involving live online meetings consist of two parts:

  1. You will be given some topics for discussion and then a link to a virtual classroom (via Adobe Connect) where you will meet with other students and your teacher and TA(s) to discuss those topics. You will need to be prepared to discuss, solve, and demonstrate all of the preparation topics. If you are not prepared you will be asked to come back another time. Inside each exploration is a link to the schedule for these meetings. Please see the rubric below to see how your work will be graded.

  2. A summary of the big idea behind the exploration. This section will contain a summary of the exploration and will aid you as a review tool. This section is not graded.
10 pointsYou will earn up to 10 points for arriving at the meeting prepared to discuss the assigned topics.
10 pointsYou will earn up to 10 points for your participation in a discussion with a small group of your peers where you will have to present your ideas and discuss the ideas of others.
10 pointsYou will earn up to 10 points for your participation in a group setting with all attendees at the online meeting.
Total30 points are possible for live online explorations.

Orientation Quiz

This course also includes a course orientation quiz. You must complete the orientation quiz with a perfect score before continuing in the course. Don't worry; the orientation quiz is not that hard and does not affect your grade. You will find the answers to the quiz questions in the Course Introduction, Syllabus, and the other menu items in the orientation module.


Summary: 1 proctored, computer-graded exam, may retake once, must pass in order to pass the course, may bring a page of notes

You must earn at least 60 percent in order to pass the exam, and you must pass the exam to pass the course. You may bring a one-sided sheet of notes and equations to the exam, see exam prep instructions for details.

Course Duration

You have 1 year to complete this course. You may purchase one 3-month extension if you need more than a year to complete this course. Because of the nature of some assignments, you will not be able to complete this course in less than 2 months.

University Policy - Title IX Statement

Preventing & Responding to Sexual Misconduct

In accordance with Title IX of the Education Amendments of 1972, Brigham Young University prohibits unlawful sex discrimination against any participant in its education programs or activities. The university also prohibits sexual harassment—including sexual violence—committed by or against students, university employees, and visitors to campus. As outlined in university policy, sexual harassment, dating violence, domestic violence, sexual assault, and stalking are considered forms of "Sexual Misconduct" prohibited by the university.

University policy requires all university employees in a teaching, managerial, or supervisory role to report all incidents of Sexual Misconduct that come to their attention in any way, including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Incidents of Sexual Misconduct should be reported to the Title IX Coordinator at or (801) 422-8692. Reports may also be submitted through EthicsPoint at or 1-888-238-1062 (24-hours a day).

BYU offers confidential resources for those affected by Sexual Misconduct, including the university’s Victim Advocate, as well as a number of non-confidential resources and services that may be helpful. Additional information about Title IX, the university’s Sexual Misconduct Policy, reporting requirements, and resources can be found at or by contacting the university’s Title IX Coordinator.

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