On this page you will find some material about Lesson 20. Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 20: Unit Circles
Learning Outcomes. (from Coburn and Herdlick’s Trigonometry book)
- Use special triangles to find points on a unit circle and locate other points using symmetry.
- Define the six trig functions in terms of a point on the unit circle.
Topic. This lesson covers
Section 3.3: The Unit Circle.
WeBWorK. There is one WeBWorK assignment on today’s material:
Video Lesson 20 (based on Lesson 20 Notes)
These are questions on fundamental concepts that you need to know before you can embark on this lesson. Don’t skip them! Take your time to do them, and check your answer by clicking on the “Show Answer” tab.
If you are not comfortable with the Warmup Questions, don’t give up! Click on the indicated lesson for a quick catchup. A brief review will help you boost your confidence to start the new lesson, and that’s perfectly fine.
Need a review? Check Lesson 14.
This is like a mini-lesson with an overview of the main objects of study. It will often contain a list of key words, definitions and properties – all that is new in this lesson. We will use this opportunity to make connections with other concepts. It can be also used as a review of the lesson.
A Quick Intro to Unit Circles
Key Words. Unit circle, reference triangle, reference angle, coterminal angle, trigonometric ratio
A unit circle is a circle with center at and radius 1. Given on the circle, we have
The right triangle on the graph is the reference triangle for the angle . It has hypotenuse 1 and legs and . So
Note that the cosine and sine values are the – and -coordinates of the point on the terminal side of that belongs to the unit circle.
In general, we have
The reference angle is a positive acute angle between the -axis and the terminal side. In the above picture, the reference angle is or .
Angles with the same reference angle have the same trig values except for their sign.
Coterminal angles have the same trigonometric values.
Many times the mini-lesson will not be enough for you to start working on the problems. You need to see someone explaining the material to you. In the video you will find a variety of examples, solved step-by-step – starting from a simple one to a more complex one. Feel free to play them as many times as you need. Pause, rewind, replay, stop… follow your pace!
A description of the video
In the video you will see how to solve
- , ,
Now that you have read the material and watched the video, it is your turn to put in practice what you have learned. We encourage you to try the Try Questions on your own. When you are done, click on the “Show answer” tab to see if you got the correct answer.
You should now be ready to start working on the WeBWorK problems. Doing the homework is an essential part of learning. It will help you practice the lesson and reinforce your knowledge.
It is time to do the homework on WeBWork:
When you are done, come back to this page for the Exit Questions.
After doing the WeBWorK problems, come back to this page. The Exit Questions include vocabulary checking and conceptual questions. Knowing the vocabulary accurately is important for us to communicate. You will also find one last problem. All these questions will give you an idea as to whether or not you have mastered the material. Remember: the “Show Answer” tab is there for you to check your work!
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