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Time Narration
00:01 Welcome to this tutorial on Introduction to Trigonometry using GeoGebra.
00:08 In this tutorial, we will learn how to construct,

A unit circle

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

GeoGebra interface

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

Ubuntu Linux OS version 14.04

GeoGebra 5.0.388.0 hyphen d.

00:43 I have already opened the GeoGebra interface.
00:47 Click on Move Graphics View tool.
00:51 Drag the origin to the centre of the Graphics view.
00:56 Under Move Graphics View, click on Zoom In tool.
01:00 Then click on screen in Graphics view.
01:03 This will magnify the Graphics view.
01:08 Click on Slider tool and then click on the screen in Graphics view.
01:16 Slider dialog appears in the Graphics view.
01:20 By default, the Number radio-button is selected.
01:24 In the Name field, type radius.
01:28 Set Minimum value as 1, Maximum value 5 and Increment of 0.1.
01:39 Click OK button.
01:41 This creates a number slider named radius.
01:45 Using the slider, radius can be changed from 1 to 5 in increments of 0.1.
01:52 Click on Slider tool and then click on the screen in Graphics view.
01:59 Slider dialog box appears.
02:01 This time, select Angle radio button.
02:05 Minimum, Max and Increment should be 0 degrees 360 degrees and 1 degree, respectively.
02:12 Click OK.
02:15 This sets up alpha slider, on which angle alpha can be changed from 0 to 360 degrees.
02:23 Click on Circle with Center and Radius tool.
02:28 Place the cursor on the origin (0,0) and click on it.
02:34 Circle with Centre and Radius text box appears.
02:39 In text box, type radius and click OK .
02:45 A circle with center A at the origin is drawn.

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

02:54 Drag the radius slider from 1 to 5 to change the radius of the circle.
03:00 Drag it to 1 to have a unit circle.
03:04 Click on Segment tool.
03:07 Click on the circumference of the circle at the x Axis.

This creates point B.

03:16 Then click on point A to draw segment AB.
03:21 Now click on Angle with Given Size tool.
03:25 Click on point B, then point A.
03:31 Angle with Given Size text-box appears.
03:35 In the text box, delete 45 degrees and select alpha α from the symbol menu.
03:43 Leave direction at counter clockwise, click OK.
03:48 Angle B prime AB is created which is equal to beta β which is equal to alpha α.
03:57 Drag the alpha α' slider from 0 to 360 degrees.
04:03 B prime moves in counter clockwise direction around the circle as alpha increases.
04:10 Now drag the alpha α slider so that beta β value is between 50 and 60 degrees.
04:18 Click on Point tool and click outside the circle to create point C.
04:26 In the Algebra view, double-click on point C to change its coordinates.
04:32 Type x B prime as x-coordinate and y-coordinate as zero and press Enter.
04:43 This will shift point C right under B prime.
04:48 Click on Segment tool.
04:51 Click on points B prime and A to join them.
04:57 This forms the hypotenuse of the right triangle A C Bprime.
05:03 Now using Segment tool join B prime and C.
05:08 A right angle is formed at C angle A C Bprime.
05:14 Angle B prime A C is equal to alpha which is equal to beta degrees.
05:21 Drag the alpha slider from 0 degree to 360 degrees to see how alpha changes.
05:30 Let us enhance the visibility of the triangle.
05:34 Double-click on angle beta β.

Click on Object properties.

05:40 Click on the Color tab.

Leave color as green.

05:45 Increase Opacity to 25.
05:49 Click on Style tab.

Increase size to 50.

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

Select Object Properties.

06:16 Click on Color tab.

Select blue.

06:20 Similarly, change the colors of C B prime to red and of AB to orange.
06:32 To rename the segments, right-click on segment A B prime.
06:39 Choose Rename option.
06:43 Type c in the name field and click OK.
06:48 Similarly, rename C B prime to a and AC to b.
06:59 If you wish, you may change the Line Thickness and the Line Style in the Style tab.
07:09 In Algebra view, click and highlight segment a.
07:13 Holding the Shift key down, highlight all 3 segments.
07:20 In Graphics view, click on Hidden option.
07:25 All three labels are hidden.
07:28 Now let us change x Axis units to radians.
07:32 Double click on x axis in Graphics view then on Object Properties.
07:39 In the Object Properties menu, click on Preferences Graphics then on x Axis.
07:47 Check the Distance option, select pi over 2.
07:53 Select the Ticks first option.
07:56 Close the Preferences box.
07:59 Units of x-axis are in radians with the intervals shown.
08:05 GeoGebra will convert degrees of angle alpha to radians.
08:11 Let us summarize.
08:13 In this tutorial, we have learnt how to use GeoGebra to construct a unit circle and a right triangle inside it.
08:22 As an Assignment,

Try constructing circles with radius 2 and 3 units.

08:29 Draw right triangles in these circles.
08:32 Also try different styles, opacity & thickness.
08:37 The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

08:45 The Spoken Tutorial Project team conducts workshops and gives certificates.

For more details, please write to us.

08:53 Please post your timed queries on this forum.
08:57 Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
09:05 More information on this mission is available at this link.
09:10 This is Vidhya Iyer from IIT Bombay signing off.

Thank you for joining.

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