Text Set #2: Trigonometric Functions and the Unit Circle

Books

Trigonometry Smarts!:

by Rebecca Wingard-Nelson

Age: 14 and up

This self-help, step-by-step book helps students learn and practice the trigonometric aspects of triangles in the unit circle in order to understand how to use sine and cosine. This book breaks down these concepts and many more into easy to follow steps, lessons, and examples for students in order for them to really learn how trigonometry works and how to feel confident when using these concepts.

Websites

Mathisfun.com: Introduction to Trigonometry:

http://www.mathsisfun.com/algebra/trigonometry.html

Age: 14 and up

This helpful website is very user-friendly which allows students to get a basic understanding of how trigonometric functions work, what they represent, and how to compute with them. There are many easy to read examples that guide students through the steps, and there is even an interactive unit circle so students can get a visual representation of the circle and how the trigonometric functions work.This is a great site for students to use outside of the classroom, as well.

The Inverse Trigonometric Functions:

http://www.mathopenref.com/triginverse.html

Age: 15-16 and up

Where there are trigonometric functions, there are their inverses. The website above shows the relationship between the trig function and its inverse, and it walks the reader through the background information, how to find them using a calculator, and how to solve with them in a written problem. It is a very supportive site that the reader can follow along with, perform problems, and read helpful hints and notes when it comes to using inverses trigonometric functions in triangles.

Trigonometric Functions:

http://www.intmath.com/trigonometric-functions/trig-functions-intro.php

Ages: 14 and up

In the opening page of this site, the title is what catches the reader. The title states, "Why learn trigonometric functions..?" I think this is a great header because many students see themselves asking this question many times, too. With this site, students read the opening page, and from there, they can explore the different aspects of trigonometric functions within this chapter of text. They have the freedom to chose where they want to go and what they want to discover, and the articles are links posted below the first page of text. These sub-articles also have great hooks to catch the reader's eye! 

The Six Trigonometric Functions and Reciprocal Functions:

http://www.regentsprep.org/regents/math/algtrig/ATT1/trigsix.htm

Ages: 14 and up 

The trig functions,along with their reciprocals, are laid out in an opening table that is great for students to read and make flashcards of if they wish. It is very spelled out for them to understand each function's parts and the parts of their reciprocal. Between the two sets, they can read and discover the relationship that they have. There are many charts that might seem overwhelming, but there are many examples for the students to work on and see how to solve problems with the functions and their reciprocals. The examples are very detailed and help students see the set up and the solution step-by-step. At the bottom, students can see how to use their calculator in order to solve the problems.  

Trigonometry Facts: Exact values of the Trigonometric Functions:

http://mathmistakes.info/facts/TrigFacts/learn/vals/sum.html

Ages: 16 and up (Students in Pre-Calculus)

With this site, students can test themselves on memorizing the values of the trigonometric functions on the unit circle where the angle and radian is presented.  It is very similar to flash cards which can be very helpful for students! The user can click the link in the box to show or hide the answer to the trig function, and they can memorize all of them! This is really useful for a pre-calculus student because they are working with the unit circle, the functions, and the values on a heavy and regular basis.

Basic Trigonometric Ratios:

http://www.purplemath.com/modules/basirati.htm

Ages: 13 and up

This is an interesting website because at the top of the page, the user is presented with two options. You can start reading the article below, or you can watch a tutorial on how to solve trigonometric ratios. I think this is neat because some students would rather read first than watch a short clip, and viseversa. The reading is very straight forward, and it is very thorough with the material. The reader discovers how trig functions came about, what they mean, how to memorize, and what the theta stands for in the function. The tables are helpful in keeping the information straight, but students might not use it. The video is also a great interactive that helps explain these same concepts.

Articles

The Tale of Unit Circle City

http://www.pixton.com/comic/11g197oo



Ages: 15 and up

Nothing beats a classic comic strip! This story of Sine and Cosine man making sure that the city of Unit Circle remains out of harms way is a great read! This comic presents trigonometric math in a very fun and exciting way that appeals to non-math students. It does include a lot of other mathematical functions such as logs, but it is still a fun read that gets students excited about reading math while giving them mathematical information.

Sine- Trigonometry for Kids!:

http://scienceforkids.kidipede.com/math/trigonometry/sine.htm

Ages: 12 and up

This article presents the use of sine, sine graph, and solving for sine in triangles in a very up-beat and engaging fashion. This site presents many topics and concepts that shows their history and how it is relevant today. There are many visuals for students to read and analyze, and the article makes excellent connections to angles and students daily lives. There is also a page for cosine and tangent for students to explore!

Trigonometry Basics Study Guide:

http://www.education.com/study-help/article/trigonometry-basics/

Ages: 14 and up

A quick and simple study guide is a great resource for students to access in any subject, but especially in math. This article gives the reader an overall lesson and refresher of trigonometric functions while helping students understand the basics of them, as well. Example problems are given and students are able to follow along or complete on their own. It is a lot to practice for students to complete, but it does cover all types of questions that they could possibly see. 

The Trig Functions- Overview: 


http://math2.org/math/algebra/functions/trig/

Ages: 14 and up

The article in this link is very straight-forward, and it is in its simplest form an overview of trigonometric functions. It also breaks down what trigonometric functions mean, how to set them up correctly, the relationships, and a written out way of how to piece together these complex functions. There is a quite a bit of reading in this article, but if there are some students who like reading, this should be a great source for them!

The Unit Circle: 

http://suite101.com/a/the-unit-circle-a64437

Ages: 15 and up

This article talks about the unit circle in its entirety, and it highlights the main points, no pun intended, of the unit circle. It also talks about how the unit circle helps us with trigonometry and when we are dealing with any right triangle. Graphing the unit circle is also a key point that this article highlights, and I think this can be useful! We don't always have time to talk about graphing the unit circle necessarily. Students are just given the unit circle and not given the time to explore with the graph. This article is easy to read, and it is enlightening, as well.

Interactives

Earth Math: 

http://earthmath.kennesaw.edu/main_site/review_topics/trig_functions.htm

Ages: 14 and up

This website is an interactive site that allows the audience to use and make connections with the unit circle and trigonometric functions. It first shows how angles in standard positions are formed in the x-y coordinate plane. Once understanding this concept, the article shows how the unit circle is derived with a simple equation. Finally, the site talks about terminal points on the unit circle, and students can click a link to participate in the interactive for terminal points on the unit circle. This interactive does have a restriction. In order to use the interactive, the user must have the updated Java software.

Inverse Sine, Cosine, and Tangent: 

http://www.mathwarehouse.com/trigonometry/inverse-sine-cosine-tangent/

Ages:  14 and up/ Teachers

Trigonometric functions are very useful, and so are their inverses. This website shows how finding the inverse compares to using the interior angle sum theorem, and it demonstrates how to use both methods. This relationship can be very helpful to see, and they do a great job at showing it. It also shows videos on how to input inverses into a calculator. There are interactive example problems for students to compute, and the site provides links to an online calculator and worksheet to practice more problems.

Degrees and Radians: 

http://www.mathinary.com/degrees_radians.jsp

Ages: 16 and up: Pre-Calculus students:

One important concept with trigonometric functions and the unit circle is converting between degrees and radians. Both of these measures are found on the unit circle, and there are ways to find them! With this site, the reader can briefly read  what each, degrees and radians, mean and how to convert either way. At the bottom, the user can use the interactive calculator to determine how to convert from degrees to radians and radians to degrees. This site is very straight forward with the reading and concepts, but it is a very good sight for those who struggle with heavy reading.

Reflection #10 Using Technology and Creditable Resources

At some point in all of our educational experiences, we all have had to analyze online resources. There are many resources out there on the world wide web that are very useful and professional in order to help people support any idea or topic that the need data or information for. However, there are also many websites that have reading material on them, but they are in no way, shape, or form useful for research purposes. This is why students are strongly discouraged from using Wikipedia. Obviously, this site is considered online reading material that is publicly well-known, but would students use this site as a creditable resource when it comes to research, writing a paper, or giving a presentation? Absolutely not. This site is not creditable enough for students to use this site, and it is important that students know how to decide which site is acceptable to use for research and what is not. In Bean, Baldwin, and Readence's Chapter 10, they offer two strategies for enhancing online reading comprehensions: SAND and ISSDAT. SAND, "helps students avoid retrieving misinformation from the Internet when they are searching for information." They must search, analyze, and note details of the sites they look up. The second strategy, ISSDAT, " helps students make intertextual connections across diverse websites when searching for a topic to be developed into a presentation, paper, or project." Here, the students must internet search, slow down, and think. After reading both of these strategies in this chapter, I think that they could come in handy when teaching the students how to conduct useful research no matter what field you are using research. At the college level, students are required to know how to research topics, and I think it is valuable to teach students these concepts in all aspects and domains during their high school career. I wouldn't particularly use this on a regular basis in my class, but I think that I could definitely mention it often.