View source for Applications-of-GeoGebra/C2/Introduction-to-Trigonometry-Using-GeoGebra/English-timed

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||'''Time'''
||'''Narration'''

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|| 00:01
|| Welcome to this tutorial on '''Introduction to Trigonometry using GeoGebra'''.

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||00:08
|| In this tutorial, we will learn how to construct, 

A unit circle

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|| 00:14
|| A right triangle inside the unit circle using '''GeoGebra'''.
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|| 00:19
|| To follow this tutorial, you should be familiar with the 

'''GeoGebra interface'''

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|| 00:26
|| basics of geometry, trigonometry and graphs.
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|| 00:31
|| Here I am using-

Ubuntu Linux OS version 14.04

GeoGebra 5.0.388.0 hyphen d.
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|| 00:43
|| I have already opened the '''GeoGebra''' interface.
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|| 00:47
|| Click on '''Move Graphics View''' tool.
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|| 00:51
|| Drag the '''origin''' to the centre of the '''Graphics''' view.
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||00:56
|| Under '''Move Graphics View''', click on '''Zoom In''' tool.

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|| 01:00
|| Then click on screen in '''Graphics''' view.

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|| 01:03
|| This will magnify the '''Graphics''' view.

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||01:08
|| Click on''' Slider''' tool and then click on the screen in '''Graphics''' view.
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|| 01:16
|| '''Slider''' dialogue appears in the '''Graphics''' view.
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|| 01:20
|| By default, the '''Number''' radio-button is selected.
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|| 01:24
|| In the '''Name''' field, type '''radius'''.
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|| 01:28
|| Set '''Minimum''' value as 1, '''Maximum''' value 5 and '''Increment''' of 0.1.
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|| 01:39
|| Click '''OK''' button.
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|| 01:41
|| This creates a '''number slider''' named '''radius'''.

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|| 01:45
|| Using the '''slider''', radius can be changed from 1 to 5 in increments of 0.1.
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|| 01:52
|| Click on '''Slider''' tool and then click on the screen in '''Graphics''' view.
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|| 01:59
|| '''Slider''' dialogue box appears.
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|| 02:01
|| This time, select '''Angle''' radio button.
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|| 02:05
|| '''Minimum, Max''' and '''Increment''' should be 0 degrees 360 degrees and 1 degree, respectively.
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|| 02:12
|| Click '''OK'''.
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|| 02:15
|| This sets up '''alpha''' slider, on which angle '''alpha ''' can be changed from 0 to 360 degrees.
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|| 02:23
|| Click on '''Circle with Center and Radius''' tool.
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|| 02:28
|| Place the cursor on the '''origin''' (0,0) and click on it.
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||02:34
|| '''Circle with Centre and Radius''' text box appears.
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||02:39
|| In text box, type '''radius''' and click '''OK''' .
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|| 02:45
|| A circle with center '''A''' at the '''origin''' is drawn.

Please note, we are using '''A''' for '''O'''(0,0).
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|| 02:54
|| Drag the '''radius''' slider from 1 to 5 to change the radius of the circle.

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|| 03:00
|| Drag it to 1 to have a unit circle.
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|| 03:04
|| Click on '''Segment''' tool.

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|| 03:07
|| Click on the circumference of the circle at the '''x Axis'''.

This creates point '''B'''.
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|| 03:16
|| Then click on point ''' A''' to draw '''segment AB'''.
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|| 03:21
|| Now click on '''Angle with Given Size''' tool.
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|| 03:25
|| Click on '''point B''', then '''point A'''.
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|| 03:31
|| '''Angle with Given Size''' text-box appears.
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|| 03:35
|| In the text box, delete '''45 degrees''' and select '''alpha α''' from the symbol menu.
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|| 03:43
|| Leave direction at '''counter clockwise''', click '''OK'''.
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||03:48
|| '''Angle B prime AB ''' is created which is equal to '''beta β''' which is equal to  '''alpha α'''.
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|| 03:57
|| Drag the '''alpha α''' slider from '''0''' to '''360 degrees''.
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||04:03
|| '''B prime''' moves in counter clockwise direction around the circle as '''alpha ''' increases.
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||04:10
|| Now drag the '''alpha α''' slider so that '''beta β''' value is between '''50''' and '''60 degrees'''.
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|| 04:18
|| Click on '''Point''' tool and click outside the circle to create '''point C'''.
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|| 04:26
|| In the '''Algebra''' view, double-click on point '''C''' to change its coordinates.
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||04:32
|| Type '''x B prime''' as '''x-coordinate''' and '''y-coordinate''' as zero and press '''Enter'''.
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|| 04:43
|| This will shift point '''C''' right under ''' B prime'''.
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|| 04:48
|| Click on '''Segment''' tool.

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|| 04:51
|| Click on points '''B prime''' and '''A''' to join them.
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||04:57
|| This forms the hypotenuse of the right triangle '''A C Bprime'''.
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||05:03
|| Now using '''Segment''' tool join '''B prime''' and '''C'''.
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|| 05:08
|| A right angle is formed at '''C''' angle '''A C Bprime'''.
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||05:14
|| Angle '''B prime A C''' is equal to '''alpha ''' which is equal to '''beta degrees'''.
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|| 05:21
|| Drag the '''alpha ''' slider from 0 degree to 360 degrees to see how '''alpha ''' changes.
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|| 05:30
|| Let us enhance the visibility of the triangle.
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|| 05:34
|| Double-click on angle '''beta β'''.

Click on '''Object properties'''.
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|| 05:40
|| Click on the '''Color''' tab.

Leave color as green.
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|| 05:45
|| Increase '''Opacity''' to 25.
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|| 05:49
|| Click on '''Style''' tab.

Increase '''size''' to 50.

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|| 05:55
|| Change the '''Decoration''' to '''arrow pointing counter clockwise'''.
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|| 06:00
|| Close the '''Preferences''' dialogue-box.
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||06:03
|| I will now change the properties of the triangle segments.
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|| 06:07
|| To change the colour of the '''segments''', double-click on '''segment A B prime'''.

Select '''Object Properties'''.
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||06:16
|| Click on '''Color''' tab.

Select '''blue'''.
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|| 06:20
|| Similarly, change the colors of '''C B prime''' to red and of '''AB''' to orange.
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|| 06:32
|| To rename the '''segments''', right-click on '''segment A B prime'''.

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|| 06:39
||Choose '''Rename''' option.

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|| 06:43
||Type '''c''' in the '''name''' field and click '''OK'''.
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|| 06:48
|| Similarly, rename '''C B prime''' to '''a''' and '''AC''' to '''b'''.
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|| 06:59
|| If you wish, you may change the '''Line Thickness''' and the '''Line Style''' in the '''Style''' tab.
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|| 07:09
|| In '''Algebra''' view, click and highlight segment '''a'''.

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|| 07:13
||Holding the '''Shift''' key down, highlight all 3 segments.
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|| 07:20
|| In '''Graphics''' view, click on '''Hidden''' option.
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|| 07:25
|| All three labels are hidden.
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|| 07:28
|| Now let us change '''x Axis''' units to '''radians'''.
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|| 07:32
|| Double click on '''x axis''' in '''Graphics''' view then on '''Object Properties'''.
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|| 07:39
|| In the '''Object Properties''' menu, click on '''Preferences Graphics''' then on '''x Axis'''.
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|| 07:47
|| Check the '''Distance''' option, select '''pi over 2'''.
 
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|| 07:53
||Select the '''Ticks''' first option.
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|| 07:56
|| Close the '''Preferences''' box.
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|| 07:59
|| Units of '''x-axis''' are in '''radians''' with the intervals shown.

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|| 08:05
||'''GeoGebra''' will convert degrees of angle '''alpha ''' to '''radians'''.
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||08:11
|| Let us summarize.
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|| 08:13
|| In this tutorial, we have learnt how to use '''GeoGebra''' to construct a unit circle and a right triangle inside it.
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|| 08:22
|| As an Assignment,

Try constructing circles with radius 2 and 3 units.

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|| 08:29
||Draw right triangles in these circles.

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|| 08:32
||Also try different styles, opacity & thickness.
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|| 08:37
|| The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.
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||08:45
|| The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.

For more details, please write to us.
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|| 08:53
|| Please post your timed queries on this forum.
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|| 08:57
|| '''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.

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|| 09:05
||More information on this mission is available at this link.
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||09:10
|| This is Vidhya Iyer from IIT Bombay signing off.

Thank you for joining.
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|}