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In this tutorial, we are going to use the *Input box* to create other mathematical objects.

We will create a point on the unit circle and trace the graph of trigonometric functions by pairing the arc length to one of its coordinates. Our partial output is shown in Figure 1.

In Figure 1, as point * C* moves counterclockwise along the circumference of the circle, point

Figure 1 - The sine wave produced by a point trace.

Instructions

1.) Open *GeoGebra*. First, we will create a point that will be the center of our unit circle. To create point * A* in the origin, type

ENTER key.

2.) Next, we construct a circle with center * A* and radius

**[A,1]** and press the ENTER key.

3.) We fix point * A* to prevent it from being accidentally moved. To fix the position of point

Figure 2 – The Properties dialog box.

4.) In *Basic tab* of the *Properties* *dialog box*, click the *Fix Object *check box to check it, then click the **Close** button.

5.) To construct point * B* at (1,0), type

6.) Fix the location of point * B* (refer to steps 3-4).

7.) To construct point * C* on the circumference of the circle, click the

Figure 3 – The unit circle with points B and C on its circumference.

8.) We will change the interval of the x-axis from **1** to **π/2.** To do this, click the **Options** menu from the menu bar, and choose **Drawing Pad** from the list do display the *Drawing pad dialog box *shown in Figure 4.

9.) In the *Axes* tab dialog box, click the *xAxis* tab.

10.) Click the *Distance* checkbox to check it and choose **π/2** from the *Distance drop-*

*down list box*.

Figure 4 – The Drawing Pad dialog box.

11.) Now we create arc * BC* of circle with center

12.) Right click the arc * BC*, you will see a dialog box as shown in Figure 5. Choose

*d* (or whatever is the name of your arc), then click **Properties** to reveal the *Properties* window.

Figure 5 – The dialog box that appears when you right click overlapping objects.

13.) In the *Properties* window, choose the *Basic tab*, be sure that the *Show label* check box is checked and choose *Value* from the drop-down list box. This will display the length of arc * BC*.

14.) Next, we change the color of the arc to make it visible. Click the *Color* tab and choose red (or any color you want) from the color palette.

15.) Click the* Style* tab, then adjust the *Line Thickness* to 5, then click the** Close** button. Your drawing should look like the one shown in Figure 6.

16.) Next, to construct the point that will trace the sine wave, we construct an ordered pair**(d,y(C)) **where **d** is the arc length and the **y(C)** y-coordinate (or sine) of point * C*.

To do this, type **P = (d,y(C)). **

**Q1: ***Move point C along the circle. What do you observe? *

17.) To trace the path point * P*, right click point P and click

**Q2: ***Now, move point C along the circumference of the circle and see the path of P.*

Figure 7 - The appearance of the drawing after Q1.

18.) To create point * Q* that will trace the cosine wave, type

19.) Activate the trace of point Q (see Step 17).

**Q3: ***Now, move point C along the circumference of the circle and observe the path of * point Q. What do you observe?

**Challenge: **Using the diagram that you have created above, graph the other four other functions namely tangent, cotangent, secant and cosecant functions.