On this page you will find some material about Lesson 23. Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 23: Trigonometric Equations
Learning Outcomes. (from Coburn and Herdlick’s Trigonometry book)
- Use a graph to gain information about principal roots, roots in ), and roots in .
- Use inverse functions to solve trig equations for the principal root.
- Solve trig equations for roots in or .
- Solve trig equations for roots in .
- Solve trig equations using fundamental identities.
- Solve trig equations using graphing technology.
Topic. This lesson covers
Section 6.3: Solving Basic Trigonometric Equations.
WeBWorK. There is one WeBWorK assignment on today’s material:
Video Lesson 23 (based on Lesson 23 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.
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 Trigonometric Equations
Key Words. Inverse trigonometric expressions, trigonometric equations, symmetry
In the Warmup Question 1, we saw that when . Equivalently, we can say
to represent the angles whose cosine is zero between 0 and .
The main idea in solving a trigonometric equation is to reduce the equation so that there is a trigonometric expression such as , and on one side, and a number on the other side.
In the above example, there are two solutions between 0 and . The calculator only provides one or value. To determine the other solution, it is useful to remember that on the unit circle, represents the cosine value and represents the sine value. For instance, if is negative, then is negative, which happens when the terminal side of is in QII or QIII. You can then use the symmetry discussed in Lesson 20 to determine all solutions.
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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