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

PoojaMoolya at 10:31, 28 October 2020

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Madhurig at 11:31, 16 February 2018

2018-02-16T11:31:14Z

Madhurig at 11:14, 16 February 2018

2018-02-16T11:14:04Z

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Nancyvarkey at 04:39, 16 February 2018

2018-02-16T04:39:14Z

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Vidhya: Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''Introduction to Trigonometry using GeoGebra''..."

2018-02-09T10:13:38Z

Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''Introduction to Trigonometry using GeoGebra''..."

New page

{|border=1
||'''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 center .
| | Drag the '''origin''' to the center 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 in '''Graphics view'''.
| | Click on''' Slider''' tool and then click on the screen in '''Graphics''' view.
|-
| | Point to the dialog box.
| | '''Slider''' dialog-box 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 this '''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 dialog box.
| | '''Slider''' dialog 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 0º, 360º and 1º, 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 0º to 360º .
|-
| | 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.
|-
| |
| | '''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 of the circle 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 '''45º''' 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 '''0º''' to '''360º'''.
|-
| |
| | '''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 '''60º'''.
|-
| | 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)''' <nowiki>=</nowiki> '''alpha αº''' which is <nowiki>= </nowiki>'''beta βº'''.
|-
| | Move the '''α''' slider from 0º to 360º .
| | Drag the '''alpha α''' slider from 0º to 360º 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''' box.
| | Close the '''Preferences''' dialog-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'''.
|-
| | 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.
|-
|}

@@ Line 55: / Line 55: @@
 || Click on''' Slider''' tool and then click on the screen in '''Graphics''' view.
 |-
-|| Point to the dialogue box.
+|| Point to the dialog box.
-|| '''Slider''' dialogue appears in the '''Graphics''' view.
+|| '''Slider''' dialog appears in the '''Graphics''' view.
 |-
 || Point to '''Number''' radio.
@@ Line 80: / Line 80: @@
 || Click on '''Slider''' tool and then click on the screen in '''Graphics''' view.
 |-
-|| Point to the dialogue box.
+|| Point to the dialog box.
-|| '''Slider''' dialogue box appears.
+|| '''Slider''' dialog box appears.
 |-
 || Click on '''Angle''' radio button.
@@ Line 213: / Line 213: @@
 || Change the '''Decoration''' to '''arrow pointing counter-clockwise'''.
 |-
-|| Close the '''Preferences''' dialogue-box.
+|| Close the '''Preferences''' dialog-box.
-|| Close the '''Preferences''' dialogue-box.
+|| Close the '''Preferences''' dialog-box.
 |-
 ||

@@ Line 20: / Line 20: @@
 '''Pre-requisites'''
-|| To follow this tutorial, you should be familiar with
+|| To follow this tutorial, you should be familiar with the
 the '''GeoGebra interface''',
 basics of geometry, trigonometry and graphs.
@@ Line 51: / Line 52: @@
 |-
-| | Click on '''Slider''' tool >> click on screen
+|| Click on '''Slider''' tool >> click on screen
-| | Click on''' Slider''' tool and then click on the screen in '''Graphics''' view.
+|| Click on''' Slider''' tool and then click on the screen in '''Graphics''' view.
 |-
 || Point to the dialogue box.
@@ Line 60: / Line 61: @@
 || By default, the '''Number''' radio-button is selected.
 |-
-|| Type Name as '''radius''' .
+|| 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.
+|| Set '''Min(minimum)''' value as 1, '''Max(maximum)''' value 5 and '''Increment''' of 0.1.
 |-
 || Click '''OK''' button.
@@ Line 86: / Line 87: @@
 |-
 || 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.
+|| '''Min(minimum), Max''' and '''Increment''' should be 0<sup>0</sup>, 360<sup>0</sup> and 1<sup>0</sup>, respectively.
 |-
 || Click '''OK'''.
@@ Line 111: / Line 112: @@
 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 >> leave it at 1.
 || Drag the '''radius''' slider from 1 to 5 to change the radius of the circle.
@@ Line 121: / Line 122: @@
 Click on the circumference of the circle at the '''x Axis'''.
-This creates '''point B'''.
+This creates point '''B'''.
 |-
-|| Click on '''point A'''.
+|| Click on point '''A'''.
 Point to '''segment AB'''.
-|| Then click on '''point A''' to draw '''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.
@@ Line 178: / Line 179: @@
 || Now using '''Segment''' tool join '''B' (B prime)''' and '''C'''.
 |-
-|| Point to the right angled triangle AB'C and its angles.
+|| Point to the right angled triangle ACB' and its angles.
 || A right angle is formed at '''C'''- angle '''ACB' (A C B prime)'''.
 |-
@@ Line 219: / Line 220: @@
 |-
 || Double click on '''segment AB'''' >> Select '''Object Properties'''.
-|| To change the color of the '''segments''', double-click on '''segment AB' (A B prime)'''.
+|| To change the colour of the '''segments''', double-click on '''segment AB' (A B prime)'''.
 Select '''Object Properties'''.