Applications-of-GeoGebra/C2/Trigonometric-Ratios-and-Graphs/English-timed

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Time Narration
00:01 Welcome to this tutorial on Trigonometric Ratios and Graphs.
00:06 In this tutorial, we will learn how to use GeoGebra to,
00:11 Calculate trigonometric ratios
00:15 Plot corresponding graphs
00:18 To follow this tutorial, you should be familiar with GeoGebra interface
00:25 Previous tutorials in this series
00:28 If not, for relevant tutorials, please visit our website
00:34 Here, I am using

Ubuntu Linux OS version 14.04

00:42 GeoGebra 5.0.388.0 hyphen d
00:48 I have opened GeoGebra interface with a unit circle and a right triangle A C Bprime.
00:59 Sine function
01:01 Sine of an angle is the ratio of the lengths of the opposite side to the hypotenuse.
01:08 Angle B prime A C is equal to alpha degrees and to beta degrees
01:15 In triangle A Bprime C, sine alpha equals ratio of the lengths B prime C to A B prime.
01:23 This is also equal to ratio of y co-ordinate of B prime to radius.
01:30 Here, sine alpha is y co-ordinate of point B prime.
01:36 Click on Options menu.
01:39 Select Rounding and then 3 Decimal Places.
01:44 All the ratios will now have 3 decimal places.
01:49 Now let us show sine alpha values using the input bar.
01:55 In input bar, type SINE is equal to y B prime in parentheses divided by radius.

Press Enter.

02:08 Sine values are displayed in Algebra view.
02:12 Drag alpha slider to 0 and then to 360 degrees.
02:20 Observe the change in sine values in Algebra view.
02:25 Observe that sine value remains positive as long as y axis values are positive.
02:32 Click on Point tool.
02:35 Click on the screen outside the circle in Graphics view.
02:40 Point D appears outside the circle.
02:44 Set alpha to 0 degrees on the slider.
02:48 Right-click on D and click on Object Properties.
02:53 Select Color tab and choose red.
02:57 Close the Preferences window.
03:00 Again, right-click on D and check Trace On option.
03:06 In Algebra view, double click on D.
03:10 Delete co-ordinates of D.
03:14 Select symbol alpha, click on the letter alpha.
03:19 Insert alpha as x co-ordinate of D.
03:23 Type SINE as y co-ordinate of D, and press Enter.
03:29 D has been changed to alpha comma SINE.
03:34 GeoGebra will convert alpha into radians.
03:39 The alpha value in radians is the x co-ordinate of D.
03:43 Its y co-ordinate is the SINE value of alpha.
03:47 This will make D trace the sine function as you change angle alpha.
03:53 We want to see 2 pi radians along the positive side of the x axis.
03:59 Under Move Graphics View, click once on Zoom Out and then twice in Graphics view.
04:09 Click on Move Graphics View tool.
04:13 Click on Graphics background and when hand symbol appears, move Graphics view.
04:20 You should see the circle and 2 pi radians along positive side of x axis.
04:29 Increase alpha on the slider from 0 to 360 degrees 2 pi radians.
04:38 Point D will trace the sine function graph.
04:42 Sine values remain positive as long as y values are positive.
04:49 In input bar, type d x in parentheses is equal to sin x in parentheses and press Enter.
05:00 Sine function will be graphed beyond minus 2 pi and plus 2 pi radians.
05:07 Click on and move Graphics view to see d of x beyond minus 2 pi and plus 2 pi radians.
05:17 Note that this will erase traces of D.
05:22 Click on and move Graphics view to see circle and plus 2 pi radians along x axis.
05:30 Again drag slider alpha to 0 degrees to see traces of D.
05:37 Compare d of x with traces of D.
05:42 Cosine function
05:44 Cosine of an angle is the ratio of the lengths of the adjacent side to the hypotenuse.
05:51 Cos alpha is equal to the following ratios.
05:55 Length of AC to length of AB prime and x co-ordinate of B prime to radius.
06:03 In this unit circle, cos alpha corresponds to x co-ordinate of point B prime.
06:10 Right-click on point D and uncheck Trace On option.
06:16 Click on and move Graphics view slightly to erase traces of D.
06:22 In input bar, type the following line.
06:26 COSINE is equal to x B prime in parentheses divided by radius.

Press Enter.

06:38 Cosine value is displayed in Algebra view.
06:42 Drag slider alpha from 0 to 360 degrees.
06:48 Observe how cosine values change in Algebra view.
06:52 Note how cosine remains positive as long as x axis values are positive.
06:59 Click on Point tool and click outside the circle.
07:05 Point E appears outside the circle.
07:08 Drag slider alpha to 0 degrees.
07:12 Right-click on E, click on Object Properties.
07:17 Select Color tab and choose brown.
07:22 Close the Preferences window.
07:25 Right-click on E, check Trace On option.
07:30 In Algebra view, double click on E.
07:34 Delete co-ordinates of E.
07:37 Select symbol alpha, click on the letter alpha.
07:43 Insert alpha as x co-ordinate of E.
07:47 Type COSINE instead of y co-ordinate of E, and press Enter.
07:55 E has been changed to alpha comma COSINE.
08:00 Drag slider alpha from 0 to 360 degrees.
08:06 Point E will trace the cosine function graph.
08:11 In input bar, type e x in parentheses is equal to cos x in parentheses.

Press Enter.

02:33 Cosine function e of x will be graphed beyond minus 2 pi and plus 2 pi radians.
08:33 Click and move Graphics view to see e of x beyond minus 2 pi and plus 2 pi radians.
08:44 This will erase traces of E.
08:48 Click on and move Graphics view to see plus 2 pi radians along x axis.
08:57 Again drag slider alpha to 0 degrees to see traces of E.
09:04 Compare the graph of e of x with traces of E.
09:09 Right-click on E and uncheck Trace On option.
09:15 Click on and move Graphics view slightly to erase traces of E.
09:21 Tangent function

Tangent of an angle is the ratio of lengths of the opposite side to the adjacent side.

09:30 Tan alpha is the ratio of sine alpha to cos alpha and the ratio of lengths of B prime C to AC.
09:39 Tan alpha is also the ratio of the y co-ordinate to x co-ordinate of B prime.
09:45 In input bar, type the following line.
09:50 TANGENT is equal to y B prime in parentheses divided by x B prime in parentheses.

Press Enter.

10:01 Tangent value is displayed in Algebra view.
10:05 Drag alpha slider from 0 to 360 degrees.
10:11 Observe how tangent values change in Algebra view.
10:15 Click on Point tool and click outside the circle.
10:21 Point F appears outside the circle.
10:24 Set alpha to 0 degrees on the slider.
10:28 Right-click on F and select Object Properties.
10:33 Select Color tab and choose green.
10:39 Close the Preferences window.
10:42 Again right-click on F, check Trace On option.
10:48 In Algebra view, scroll down and double click on F.
10:54 Delete co-ordinates of F.
10:58 Select symbol alpha, click on the letter alpha.
11:03 Insert alpha as x co-ordinate of F.
11:07 Type TANGENT as y co-ordinate of F, and press Enter.
11:13 F has been changed to alpha comma TANGENT.
11:18 Point F will trace the tangent function graph as alpha value changes.
11:24 Increase alpha on the slider from 0 to 360 degrees 2 pi radians.
11:32 F increases from origin to infinity.
11:37 Note vertical asymptote at pi divided by 2 radians.
11:42 Tangent value is plus infinity at pi divided by 2 radians.
11:49 It is minus infinity at 3 pi divided by 2 radians.
11:55 In input bar, type f x in parentheses is equal to tan x in parentheses and press Enter.
12:07 The tangent function is graphed beyond minus 2 pi and plus 2 pi radians.
12:16 Click on and move Graphics view to see graph of f of x beyond minus 2 pi and plus 2 pi radians.
12:28 Click on and move Graphics view to see plus 2 pi radians along x axis.
12:37 Drag slider alpha back to 0 degrees to see traces of F.
12:43 Also compare the tangent function f of x with traces of F.
12:50 Let us summarize.
12:52 In this tutorial, we have learnt

how to use GeoGebra to calculate and graph sin alpha, cos alpha and tan alpha

13:03 Assignment

Try these steps to graph secant, cosecant and cotangent functions.

13:12 Analyze the link between sine values for supplementary angles

angles whose sum is 180 degrees.

13:21 Analyze the link between sine and cosine values for supplementary angles.
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14:01 This is Vidhya Iyer from IIT Bombay signing off.

Thank you for joining.

Contributors and Content Editors

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