|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
|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.|
|02:15||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.
|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.|
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|09:10|| This is Vidhya Iyer from IIT Bombay signing off.
Thank you for joining.