Trigonometry Online Resource Library

This is an online resource library for other teachers of secondary mathematics.  The purpose of this page is to provide teachers with different sites and applets they can use to enhance student understanding.  This page is specifically designed for teachers of trigonometry.  The following are link about material in trigonometry.  I have found that students struggle with trigonometry the first time around, so I have done some research and observed some applets that I believe will enhance student understanding.  The following are the links.

1. Sine Box—This page is designed to show how the values of sine are determined at different angles.  students are able to input the angle measure (in degrees) and the applet shows the angle opening up to that and then showing what the value of sin is and how it it is determined.
2. Cosine Box—This page is designed to show how the values of cosine are determined at different angles.  Students are able to input the angle measure (in degrees) and the applet shows the angle opening up to that and then showing what the value of cos is and how it it is determined.
3. Six Trig Functions—This site you are able to drag the point on the outside of the unit circle and to see how the values of either, sine, cosine, tangent, cosecant, secant and cotangent change as the point moves.  Everything is in decimal format and the angles are measured in degrees.  Great to show students how things change but not great if you want to stick with the exact value on the unit circle.
4. Graph of y=sinx—This is an excellent applet to show students (especially if you have a smartboard or a way to project from your computer to the class) how the graph of y=sinx is created.  I have found in the past some students can visualize what is going on but most have a difficult time with this concept.
5. Graph y=cosx—This applet, in my opinion, is not as good as the one for sine.  The – is rotated as is the unit circle.  i could some students confused by this.  It does a great job of showing the changes that are taking place and the students can slow the animation so it will go slower and the student can really observe the changes that are taking place.
6. Graph of y=tanx—This applet is designed to help students understand where the graph of tangent comes from.  I have always found this one of the hardest things for students to visualize.  The reason this is because they have to imagine the values of both x and y as the angel changes and think about the ration of x:y.  Tremendously difficult concept to gain the grasp of for students.  I have tried to explain this in the past but I feel this applet does a great job in showing the changes that take place.  It would also be a great calculus concept in seeing how they values change with the angle measure.
7. Graph of y=sin ax–This applet is designed to show students how the graphs of y=sinx and y=sin ax differ.  Students can draw the graph with a values ranging from -4 to 3.9.  Both graphs are graphed at the same time and in different colors to enhance student understanding.  Really powerful for the initial graphing and to go over what that value of z means and a great thing to go over when solving trig equations to show how many answers would exist when the domain goes from 0 to 360 degrees.
8. Transformations of sine and cosine —This applet is designed to show some of the transformations that can take place.  The graph is already drawn and it is in degrees.  The students can change the a value b value and c value and observe the changes that take place.  There is no vertical shift though.  it has its limits but still good for students observe multiple changes taking place at once.
9. Sin t=a—-This applet is designed to allow students to guess angles measures in degrees for sine, given what sine of some unknown angle equals.  The great thing about this applet is that it provides a visual representation of the height of the a value and students input their angle guess and point moves along the unit circle until it reaches that angle and it gives you the value of a at that angle and students can keep guessing until they get it and then they can move onto the next value for a.  The students can put in angle measures from -360 to 360 degrees.  A teachable moment would be to ask students when they get the right answer if that is the only correct answer or are their others.  You readdress coterminal angles at this point.  Drawback for this site is the use of only degrees.
10. Right Triangle Trigonometry—This applet is excellent to show students the changes that take place when you change the angle measure from 1 to 89 degrees.  You can see the changes of sine, cosine and tangent simultaneously as the angel changes.  Tough thing for many students to visualize at this level but great thing to be able to see.  Once again a great activity to show how changes affect each one differently and have students put some reason behind this.
11. Graphs of Sine and Cosine and translations of both—–This applet is designed to help students see the graphs of sine and cosine and the transformations that can be applied.  All of the angle measures are in radians.  Students are asked to manipulate the functions and see the results of their manipulations.  There is a wealth of vocabulary that is addressed as well.  Students can see the highlighted vocabulary followed by written definitions and examples explaining the definitions.
12. Unit Circle and the Trig Functions sin(x), cos(x) and tan (x )  –Students explore the values of sin(x), cos(x) and tan(x) as a point on the unit circle is moved.  Students can see where the graphs come from as well as observing the unit circle.
13. Graphs of y=a sin x and y=a cos x—This is a great website that starts students with the beginning stages of graphing sine and cosine and having the ability to change the amplitude.  there are explanations (written in paragraph form) to help the students understand what is going on with guiding questions and a synopsis.  There are five problems at the bottom that students are encouraged to complete.
14. Exploring the Unit Circle—This applet allows students to explore the values of x and y on the unit circle as a point on the outside of the unit circle is rotated.  Students can change from degree to radian mode.  the radians are given in decimals as are the values of x and y.  the exact values are not given and students cannot input an angle.  They can drag the point.  I would go over this after explaining the unit circle in class and having the students change the exact value answers to decimals and the radians to decimals. this will help with student understanding.
15. Exploring the graphs of y=sinx and y=cos x—This applet allows students to explore how the graphs of sine and cosine with the unit circle.  The amplitude is one and cannot be changed and the graphs of sine and cosine are already drawn.  The student drags a point along the unit circle and sees that point being moved on the graph.  There is not much work the student must do accept observe what is taking place.  I would only use the site to show students the relationship between the point on the unit circle and the points of the graph.  In class it is impossible to sketch every point and the unit circle has certain significant points but it is nice for the students to see the continuity of this and to observe the repeating pattern begins after one revolution of a circle.
16. Transformations of Sine—This is an excellent applet.  It starts with the graph of y=sin x and then students can manipulate the values of to observe how the graph is changes.  Students will have to be well versed in the graph of the sine function before they approach this applet.  Please click here for the worksheet/lesson plan that accompanies this exploration.
17. Transformations of Cosine—- This is an excellent applet. It starts with the graph of y=cos x and then students can manipulate the all the different values to observe how the graph is transformed.  There are some restrictions on values that can be used because of the limited size graphs, but all the values can be manipulated at once.
18. Graphs of tangent, cosecant, secant and cotangent–This is an good applet for going over the graphs of tangent, cosecant, secant and cotangent.  Students are able to use the applet to distinguish the the difference between the base graph and horizontal transformations.  There are no vertical transformations that can be applied.
19. Polar Coordinates and graphs–This applet is designed to show students what a polar graph looks like.  Students should be expected to have some experience with knowing what a polar coordinate is and how to graph a point.  Students can input any polar equation they want.  The graph will appear immediately.  There is also a table that will students can click on a table will appear.
20. Graphs of sine, cosine, tangent, cosecant, secant and cotangent—This applet allows students to see the graphs of all six at once or one or more at a time with different colors.  Not the best.  No transformations.  But might be a good applet to use when just beginning.  I would go over the unit circle with them first and go over asymptotes and dividing by zero.