View source for 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''' value as 1, '''Max''' 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, Max''' and '''Increment''' should be 0<sup>0</sup>, 360<sup>0</sup> and 1<sup>0</sup>, 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 0<sup>0</sup> to 360<sup>0</sup>.
|-
|| 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 but leave it at 1 finally.
|| 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 '''45<sup>0</sup>''' 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 '''0<sup>0</sup>''' to '''360<sup>0</sup>'''.
|-
||
|| '''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 '''60<sup>0</sup>'''.
|-
|| 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 AB'C 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 α<sup>0</sup>''' which is equal to '''beta β<sup>0</sup>'''.
|-
|| Move the '''α''' slider from 0<sup>0</sup> to 360<sup>0</sup>.
|| Drag the '''alpha α''' slider from 0<sup>0</sup> to 360<sup>0</sup> 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 color 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'''.
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|| 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'''
|| The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.
|-
|| '''Slide Number 8'''

'''Spoken Tutorial workshops'''
|| The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.


For more details, please write to us.
|-
|| '''Slide Number 9'''

'''Forum for specific questions:'''

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them

|| Please post your timed queries on this forum.
|-
|| '''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.
|-
|}