Precalculus II

Purpose of Course  showclose

Precalculus II continues the in-depth study of functions addressed in Precalculus I by adding the trigonometric functions to your function toolkit. In this course, you will cover families of trigonometric functions, as well as their inverses, properties, graphs, and applications. Additionally, you will study trigonometric equations and identities, the laws of sines and cosines, polar coordinates and graphs, parametric equations and elementary vector operations.

You might be curious how the study of trigonometry, or “trig,” as it is more often referred to, came about and why it is important to your studies still. Trigonometry, from the Greek for “triangle measure,” studies the relationships between the angles of a triangle and its sides and defines the trigonometric functions used to describe those relationships. Trigonometric functions are particularly useful when describing cyclical phenomena and have applications in numerous fields, including astronomy, navigation, music theory, physics, chemistry, and – perhaps most importantly, to the mathematics student – calculus.

In this course, you will begin by establishing the definitions of the basic trig functions and exploring their properties and then proceed to use the basic definitions of the functions to study the properties of their graphs, including domain and range, and to define the inverses of these functions and establish the properties of these. Through the language of transformation, you will explore the ideas of period and amplitude and learn how these graphical differences relate to algebraic changes in the function formulas. You will also learn to solve equations, prove identities using the trig functions, and study several applications of these functions.

Course Information  showclose

Welcome to MA003. General information on this course and its requirements can be found below. Please keep in mind that this course is designed to support your ability to succeed in other college courses. You will benefit from this course by taking it before or during your college studies.

Course Designers: Alessandra Bianchini

Primary Resources: This course is comprised of a range of different free, online materials. However, the course makes primary use of the following materials:

Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials. Most units will require you to complete checkpoint exercises that review the textbook information as well as self-reflective short answer questions that ask you to apply the information. In addition to these, you will also need to complete the Final Exam.

Note that you will only receive an official grade on your final exam. However, in order to adequately prepare for this exam, you will need to have a strong command of all the material covered in the course. The most efficient and effective way for you to learn this material is to simply work through all the units and complete all the activities as the instructor and course designer have presented them.

In order to pass this course, you will need to earn a 70% or higher on the Final Exam, which is administered electronically through the Moodle system. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.

Time Commitment: This course should take you approximately 72 hours to complete. Each unit includes a time advisory that lists the amount of time you should expect to spend on each subunit. These are only approximate times meant to help you plan your time accordingly, and could vary considerably for you. Please particularly note that the time commitment for each unit varies significantly; for example, Unit 2 should take you less than 15 hours, while Unit 4 will likely take you 25 hours.
It is a good idea to use the time estimates to help you plan in advance when you will find time to complete each unit. It may be useful to take a look at these time advisories and to determine how much time you have over the next few weeks to complete each unit, and then to set goals for yourself.

For example, Unit 1 should take you 17 hours. Perhaps you can sit down with your calendar and decide to complete subunits 1.1 and 1.2 (a total of 6 hours) on Monday night; subunit 1.3 (a total of 3 hours) on Tuesday night; etc.

Tips/Suggestions: The skills and concepts that you learn in this course are designed to be applied to all the other courses you will take during your college experience. As you complete each unit, look for ways to immediately apply that unit’s main ideas to other work you are doing.

This course has been developed through a partnership with the Washington State Board for Community and Technical Colleges. Unless otherwise noted, all materials are licensed under a Creative Commons Attribution 3.0 Unported License. The Saylor Foundation has modified some materials created by the Washington State Board for Community and Technical Colleges in order to best serve our users.

Khan Academy  
This course features a number of Khan Academy™ videos. Khan Academy™ has a library of over 3,000 videos covering a range of topics (math, physics, chemistry, finance, history and more), plus over 300 practice exercises. All Khan Academy™ materials are available for free at

Learning Outcomes  showclose

Upon successful completion of this course, the student will be able to:

  • measure angles in degrees and radians, and relate them to arc length;
  • solve problems involving right triangles and unit circles using the definitions of the trigonometric functions;
  • solve problems involving non-right triangles;
  • relate the equation of a trigonometric function to its graph;
  • solve trigonometric equations using inverse trig functions;
  • prove trigonometric identities;
  • solve trig equations involving identities;
  • relate coordinates and equations in Polar form to coordinates and equations in Cartesian form;
  • perform operations with vectors and use them to solve problems;
  • relate equations and graphs in Parametric form to equations and graphs in Cartesian form;
  • link graphical, numeric, and symbolic approaches when interpreting situations and analyzing problems;
  • write clear, correct, and complete solutions to mathematical problems using proper mathematical notation and appropriate language; and
  • communicate the difference between an exact and an approximate solution and determine which is more appropriate for a given problem.

Course Requirements  showclose

In order to take this course you must:
√    have access to a computer;
√    have continuous broadband Internet access;
√    have the ability/permission to install plug-ins or software (e.g., Adobe Reader or Flash);
√    have the ability to download and save files and documents to a computer;
√    have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.);
√    be competent in the English language; and
√    have read the Saylor Student Handbook.

Unit Outline show close