Lesson 2:

The purpose of this lesson is to help the student understand better some of the concepts on trigonometry.

In this lesson, we will go some of the basic identities in trigonometry. The following is a list of basic identifies I will go through with the JAVA applet.

Please bring up the JAVA applet. First, let's try to get the cosecant function on the graph window.

  1. Enter or choose 1 at the amplitude box.
  2. Enter "0" for the frequency box and choose the wave form as cosine. We know that the cosine of 0 is 1. So these give us the 1 constant in the graph window after you click on the "CLEAR" and "+" buttons.
  3. At this point, we should obtain a sine wave with amplitude of 1. A good frequency value will probably be around 5.
  4. Click on the "/" button instead of the "CLEAR" and "+" buttons. The resultant graph should give you the cosecant function as shown in figure 1.

Fig 1.


Let's try again with the JAVA applet to bring the tangent function.

  1. Enter a frequency of 5 Hz, amplitude of 1, and wave form as sine.
  2. Click on the "CLEAR", then the "+" button to get the wave display on the graph window.
  3. To obtain the cosine wave, simply change the wave form on the applet to cosine.
  4. Remember that we want a sine dividing a cosine, so after the cosine wave is displayed, click on the "/" button to obtain the tangent wave.

The result of the tangent wave is shown in figure 2.

Fig 2.


You may want to tried to see if you are able to get the cotangent graph as in figure 3.

(Note: The JAVA applet can not do 1/tan(x) at this point. This is one of the limitations. However, you can achieve the result easily with a bit manipulation)

Fig 3.


At this point, you should be able to create some basic functions of sine and cosine waves.

I like to take this chance to prove some of the identities in your trigonometry class with the JAVA page.

The first identity is sin^2(x) + cos ^2(x) = 1. In the JAVA applet, I enter the following instructions.

  1. Amplitude=3, frequency=5, and wave form is sine. I also choose the power of 2 in the power box.
  2. Click on the "CLEAR" and then the "+" button to obtain figure 4.
  3. Then I changed the wave form to cosine so figure 5 is obtained.
  4. Then I click on the "+" button to obtained a constant of 9. The resultant graph is displayed in figure 6.

This proves one of the trigonometry identities.


Fig 4.


Fig 5.


Fig 6.


I will leave the other two identities for you to play in with the JAVA applet.

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