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

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.

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