Applications-of-GeoGebra/C2/Introduction-to-Trigonometry-Using-GeoGebra/English

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Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Introduction to Trigonometry using GeoGebra.
Slide Number 2

Learning Objectives

In this tutorial, we will learn how to construct,

A unit circle

A right triangle inside the unit circle using GeoGebra.

Slide Number 3

Pre-requisites

To follow this tutorial, you should be familiar with the

GeoGebra interface,

basics of geometry, trigonometry and graphs.

Slide Number 4

System Requirement

Here I am using-

Ubuntu Linux OS version 14.04

GeoGebra 5.0.388.0-d.

Show the GeoGebra window. I have already opened the GeoGebra interface.
Click on Move Graphics View tool. Click on Move Graphics View tool.
Drag the origin to the centre. Drag the origin to the centre of the Graphics view.
Click on Zoom In tool >> click on screen in Graphics view. Under Move Graphics View, click on Zoom In tool.

Then click on screen in Graphics view.

This will magnify the Graphics view.

Click on Slider tool >> click on screen Click on Slider tool and then click on the screen in Graphics view.
Point to the dialogue box. Slider dialogue appears in the Graphics view.
Point to Number radio. By default, the Number radio-button is selected.
Type Name as radius . In the Name field, type radius.
Change Min, Max and Increment values. Set Min(minimum) value as 1, Max(maximum) value 5 and Increment of 0.1.
Click OK button. Click OK button.
Point to the slider.

Drag to show the changing values.

This creates a number slider named radius.

Using the slider, radius can be changed from 1 to 5 in increments of 0.1.

Click on Slider tool >> click on screen in Graphics view. Click on Slider tool and then click on the screen in Graphics view.
Point to the dialogue box. Slider dialogue box appears.
Click on Angle radio button. This time, select Angle radio button.
Change Min, Max and Increment values. Min(minimum), Max and Increment should be 00, 3600 and 10, respectively.
Click OK. Click OK.
Drag to show the changing values. This sets up alpha slider, on which angle alpha (α) can be changed from 00 to 3600.
Click on Circle with Center and radius tool. Click on Circle with Center and Radius tool.
Place the cursor on the origin and click on it. Place the cursor on the origin (0,0) and click on it.
Text box Circle with Centre and Radius text box appears.
Type radius in the text box, click OK. In text box, type radius and click OK .
Point to the circle at the center. A circle with center A at the origin is drawn.

Please note, we are using A for O(0,0).

Drag the radius slider from 1 to 5 >> leave it at 1. Drag the radius slider from 1 to 5 to change the radius of the circle.

Drag it to 1 to have a unit circle.

Click on Segment tool >> click on circumference at the x axis. Click on Segment tool.

Click on the circumference of the circle at the x Axis.

This creates point B.

Click on point A.

Point to segment AB.

Then click on point A to draw segment AB.
Click on Angle with Given Size tool. Now click on Angle with Given Size tool.
Click on point B >> point A. Click on point B, then point A.
Point to the Angle with Given Size. Angle with Given Size text-box appears.
Point to Angle with Given Size text box. In the text box, delete 450 and select alpha α from the symbol menu.
Point to counter-clockwise radio button. Leave direction at counter-clockwise, click OK.
Angle B'AB (B prime A B) is created which is = beta β which is = alpha α.
Drag the α slider. Drag the alpha α slider from 00 to 3600.
B' (B prime) moves in counter clockwise direction around the circle as alpha α increases.
(ideal angle is between 50-60 degree) Now drag the alpha α slider so that beta β value is between 50 and 600.
Click on Point tool>> click outside the circle >> Point to point C. Click on Point tool and click outside the circle to create point C.
Double click on C in the Algebra view. In the Algebra view, double-click on point C to change its coordinates.
Change co-ordinates of point C to (x(B'), 0) >> press enter. Type x(B') (x B prime) as x-coordinate and y-coordinate as zero and press Enter.
Move the cursor to point C. This will shift point C right under B' (B prime).
Click on Segment tool >> click on points B' and A. Click on Segment tool.

Click on points B' (B prime) and A to join them.

This forms the hypotenuse of the right triangle ACB' (A C B prime).
Click on Segment tool >> click on points B' and C. Now using Segment tool join B' (B prime) and C.
Point to the right angled triangle ACB' and its angles. A right angle is formed at C- angle ACB' (A C B prime).
Angle B'AC (B prime A C) is equal to alpha α0 which is equal to beta β0.
Move the α slider from 00 to 3600. Drag the alpha α slider from 00 to 3600 to see how alpha α changes.
Formatting the triangle Let us enhance the visibility of the triangle.
Double click on angle β >> Select Object Properties. Double-click on angle beta β.

Click on Object properties.

Click on Color tab. Click on the Color tab.

Leave color as green.

Drag the Opacity slider to 25. Increase Opacity to 25.
Click on Style tab >> drag size slider to 50. Click on Style tab.

Increase size to 50.

Change Decoration to arrow pointing counter-clockwise. Change the Decoration to arrow pointing counter-clockwise.
Close the Preferences dialogue-box. Close the Preferences dialogue-box.
I will now change the properties of the triangle segments.
Double click on segment AB' >> Select Object Properties. To change the colour of the segments, double-click on segment AB' (A B prime).

Select Object Properties.

Click on Color tab and select blue. Click on Color tab.

Select blue.

Double click on segment CB'>> Select Object Properties.

Click on Color tab and select red.

Double click on segment AB>> Select Object Properties.

Click on Color tab and select orange.

Similarly, change the colors of CB' (C B prime) to red and of AB to orange.
Right-click on segment AB'>> Rename >> type c in name field >> click OK. To rename the segments, right-click on segment AB' (A B prime).

Choose Rename option.

Type c in the name field and click OK.

Right-click on segment CB' >> Rename >> type a in name field >> click OK.

Right-click on segment AC >> Rename >> type b in name field >> click OK.

Similarly, rename CB' (C B prime) to a and AC to b.
Click on style tab >> point to line thickness and line style options. If you wish, you may change the Line Thickness and the Line Style in the Style tab.
In Algebra view, click and highlight segment a. In Algebra view, click and highlight segment a.
Holding Shift key down, drag and highlight b and c as well. Holding the Shift key down, highlight all 3 segments.
In Graphics view, click on Hidden option. In Graphics view, click on Hidden option.
Point to the segments in Graphics view. All three labels are hidden.
Switching x axis to radians Now let us change x Axis units to radians.
Double click on x axis in Graphics view >> Object properties. Double click on x axis in Graphics view then on Object Properties.
Click on Preferences-Graphics >> x axis. In the Object Properties menu, click on Preferences-Graphics then on x Axis.
Check the Distance option, select π/2 >> select Ticks first option. Check the Distance option, select pi over 2.

Select the Ticks first option.

Close the Preferences box. Close the Preferences box.
Point to x-axis. Units of x-axis are in radians with the intervals shown.

GeoGebra will convert degrees of angle alpha α to radians.

Let us summarize.
Slide Number 5

Summary

In this tutorial, we have learnt how to use GeoGebra to construct a unit circle and a right triangle inside it.
Slide Number 6

Assignment

As an Assignment,

Try constructing circles with radius 2 and 3 units.

Draw right triangles in these circles.

Also try different styles, opacity & thickness.

Slide Number 7

About Spoken Tutorial project

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Slide Number 8

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Slide Number 9

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Slide Number 10

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Vidhya Iyer from IIT Bombay signing off.

Thank you for joining.

Contributors and Content Editors

Madhurig, Nancyvarkey, Vidhya