| Slide Number 1
|Welcome to this tutorial on Introduction to Trigonometry using GeoGebra.|
| Slide Number 2
| In this tutorial, we will learn how to construct,
A unit circle
A right triangle inside the unit circle using GeoGebra.
| Slide Number 3
| To follow this tutorial, you should be familiar with the
basics of geometry, trigonometry and graphs.
| Slide Number 4
| Here I am using-
Ubuntu Linux OS version 14.04
|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.
| 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
|In this tutorial, we have learnt how to use GeoGebra to construct a unit circle and a right triangle inside it.|
| Slide Number 6
| 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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Please download and watch it.
| Slide Number 8
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| Slide Number 9
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Please visit this site
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Explain your question briefly
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|Please post your timed queries on this forum.|
| Slide Number 10
| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
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| This is Vidhya Iyer from IIT Bombay signing off.
Thank you for joining.