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

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||'''Time'''
||'''Narration'''

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|| 00:01
|| Welcome to this tutorial on '''Trigonometric Ratios and Graphs'''.
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|| 00:06
|| In this '''tutorial''', we will learn how to use '''GeoGebra''' to,

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|| 00:11
|| Calculate '''trigonometric ratios'''

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|| 00:15
|| Plot corresponding graphs
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|| 00:18
|| To follow this '''tutorial''', you should be familiar with '''GeoGebra''' interface

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|| 00:25
|| Previous '''tutorials''' in this series

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|| 00:28
|| If not, for relevant '''tutorials''', please visit our website 
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||00:34
|| Here, I am using

'''Ubuntu Linux OS version 14.04'''

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|| 00:42
|| '''GeoGebra 5.0.388.0 hyphen d'''
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|| 00:48
|| I have opened '''GeoGebra''' interface with a '''unit circle''' and a right triangle '''A C Bprime.'''
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|| 00:59
||'''Sine function'''

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|| 01:01
|| '''Sine''' of an angle is the ratio of the lengths of the opposite side to the '''hypotenuse'''.

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|| 01:08
|| '''Angle B prime A C''' is equal to '''alpha degrees''' and to '''beta degrees'''

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||01:15 
|| In '''triangle A Bprime C''', '''sine alpha''' equals ratio of the lengths ''' B prime C''' to '''A B prime'''.

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|| 01:23
|| This is also equal to ratio of '''y co-ordinate''' of '''B prime''' to '''radius'''.

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|| 01:30
|| Here, '''sine alpha''' is '''y co-ordinate''' of point '''B prime'''.
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|| 01:36
|| Click on '''Options''' menu.

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|| 01:39
|| Select '''Rounding''' and then '''3 Decimal Places'''.

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|| 01:44
|| All the ratios will now have 3 decimal places.
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|| 01:49
|| Now let us show '''sine alpha''' values using the '''input bar'''.

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|| 01:55
|| In '''input bar''', type '''SINE''' is equal to '''y B prime''' in parentheses divided by '''radius'''.

Press '''Enter'''.
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|| 02:08
|| '''Sine''' values are displayed in '''Algebra''' view.
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|| 02:12
|| Drag '''alpha slider''' to 0 and then to 360 '''degrees'''.
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||02:20
|| Observe the change in '''sine''' values in '''Algebra''' view.

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|| 02:25
|| Observe that '''sine''' value remains positive as long as '''y axis''' values are positive.
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|| 02:32
||Click on '''Point''' tool.

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|| 02:35
|| Click on the screen outside the circle in '''Graphics view.'''
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|| 02:40
|| Point '''D''' appears outside the circle.
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|| 02:44
|| Set '''alpha''' to 0 '''degrees''' on the '''slider'''.
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|| 02:48
|| Right-click on '''D''' and click on '''Object Properties'''.

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|| 02:53
|| Select '''Color''' tab and choose red.
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|| 02:57
|| Close the '''Preferences''' window.
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|| 03:00
|| Again, right-click on '''D''' and check '''Trace On''' option.
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|| 03:06
|| In '''Algebra''' view, double click on '''D'''.
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|| 03:10
|| Delete '''co-ordinates''' of '''D'''.
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|| 03:14
|| Select '''symbol alpha''', click on the letter '''alpha'''.

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|| 03:19
|| Insert '''alpha''' as '''x co-ordinate''' of '''D'''.
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||03:23
|| Type '''SINE''' as '''y co-ordinate''' of '''D''', and press '''Enter'''.
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|| 03:29
|| '''D''' has been changed to '''alpha comma SINE'''.
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||03:34
|| '''GeoGebra''' will convert '''alpha''' into '''radians'''.

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|| 03:39
|| The '''alpha''' value in '''radians''' is the '''x co-ordinate''' of '''D'''.

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|| 03:43
|| Its '''y co-ordinate''' is the '''SINE''' value of '''alpha'''.

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|| 03:47
|| This will make '''D''' trace the '''sine function''' as you change '''angle alpha'''.
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||03:53
|| We want to see 2 '''pi radians''' along the positive side of the '''x axis'''.
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|| 03:59
|| Under '''Move Graphics View''', click once on '''Zoom Out''' and then twice in '''Graphics''' view.
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|| 04:09
|| Click on '''Move Graphics View''' tool.

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|| 04:13
|| Click on '''Graphics''' background and when hand '''symbol''' appears, move '''Graphics''' view.
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|| 04:20
|| You should see the circle and 2 '''pi radians''' along positive side of '''x axis'''.
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|| 04:29
|| Increase '''alpha''' on the '''slider''' from 0 to 360 '''degrees''' 2 '''pi radians'''.
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||04:38
|| Point '''D''' will trace the '''sine function''' graph.
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|| 04:42
|| '''Sine''' values remain positive as long as '''y''' values are positive.
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|| 04:49
|| In '''input bar''', type '''d x''' in parentheses is equal to '''sin x''' in parentheses and press '''Enter'''.
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|| 05:00
|| '''Sine function''' will be graphed beyond '''minus 2 pi''' and '''plus 2 pi radians'''.
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|| 05:07
|| Click on and move '''Graphics''' view to see '''d of x''' beyond '''minus''' 2 '''pi''' and '''plus''' 2 '''pi radians'''.
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|| 05:17
|| Note that this will erase traces of '''D'''.
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|| 05:22
|| Click on and move '''Graphics''' view to see circle and '''plus''' 2 '''pi radians''' along '''x axis'''.
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|| 05:30
|| Again drag '''slider alpha''' to 0 '''degrees''' to see traces of '''D'''.
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|| 05:37
|| Compare '''d of x''' with traces of '''D'''.
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|| 05:42
||'''Cosine function'''

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|| 05:44
|| '''Cosine''' of an angle is the ratio of the lengths of the adjacent side to the '''hypotenuse'''.

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|| 05:51
|| '''Cos alpha''' is equal to the following ratios.

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|| 05:55
|| Length of '''AC to''' length of '''AB prime''' and '''x co-ordinate''' of '''B prime''' to '''radius'''.

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|| 06:03
|| In this '''unit circle, cos alpha''' corresponds to '''x co-ordinate''' of point '''B prime.'''
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|| 06:10
|| Right-click on point '''D''' and uncheck '''Trace On''' option.
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|| 06:16
|| Click on and move '''Graphics''' view slightly to erase traces of '''D'''.
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|| 06:22
|| In '''input bar''', type the following line.

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|| 06:26
|| '''COSINE''' is equal to '''x B prime''' in parentheses divided by '''radius'''.

Press '''Enter'''.
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|| 06:38
|| '''Cosine''' value is displayed in '''Algebra''' view.
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|| 06:42
|| Drag '''slider alpha''' from 0 to 360 '''degrees'''.
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|| 06:48
|| Observe how '''cosine''' values change in '''Algebra''' view.
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|| 06:52
|| Note how '''cosine''' remains positive as long as '''x axis''' values are positive.
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|| 06:59
||Click on '''Point''' tool and click outside the circle.

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||07:05 
|| '''Point E''' appears outside the circle.
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|| 07:08
|| Drag '''slider alpha''' to 0 '''degrees'''.
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|| 07:12
|| Right-click on '''E''', click on '''Object Properties'''.

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|| 07:17
|| Select '''Color''' tab and choose brown.
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|| 07:22
|| Close the '''Preferences''' window.
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|| 07:25
|| Right-click on '''E''', check '''Trace On''' option.
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|| 07:30
|| In '''Algebra''' view, double click on '''E'''.
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|| 07:34
|| Delete '''co-ordinates''' of '''E'''.
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|| 07:37
|| Select '''symbol alpha''', click on the letter '''alpha'''.

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|| 07:43
|| Insert '''alpha''' as '''x co-ordinate''' of '''E'''.
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|| 07:47
|| Type '''COSINE''' instead of '''y co-ordinate''' of '''E''', and press '''Enter'''.
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||07:55
|| '''E''' has been changed to '''alpha comma COSINE'''.
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|| 08:00
|| Drag '''slider alpha''' from 0 to 360 '''degrees'''.
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|| 08:06
|| Point '''E''' will trace the '''cosine function''' graph.
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|| 08:11
|| In input bar, type '''e x in parentheses is equal to cos x in parentheses'''.

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

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

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|| 09:30
|| '''Tan alpha''' is the ratio of '''sine alpha''' to '''cos alpha''' and the ratio of lengths of '''B prime C''' to '''AC'''.

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|| 09:39
|| '''Tan alpha''' is also the ratio of the '''y co-ordinate''' to '''x co-ordinate''' of '''B prime'''.
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|| 09:45
|| In '''input bar''', type the following line.

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|| 09:50
|| '''TANGENT''' is equal to '''y B prime''' in parentheses divided by '''x B prime''' in parentheses.

Press '''Enter'''. 

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|| 10:01
|| '''Tangent''' value is displayed in '''Algebra''' view.
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|| 10:05
|| Drag '''alpha slider''' from 0 to 360 '''degrees'''.
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|| 10:11
|| Observe how '''tangent''' values change in '''Algebra''' view.
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|| 10:15
|| Click on '''Point''' tool and click outside the circle.
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|| 10:21
|| Point '''F''' appears outside the circle.
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|| 10:24
|| Set '''alpha''' to 0 '''degrees''' on the '''slider'''.
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||10:28
|| Right-click on '''F''' and select '''Object Properties'''.

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|| 10:33
|| Select '''Color''' tab and choose green.
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||10:39
|| Close the '''Preferences''' window.
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|| 10:42
|| Again right-click on '''F''', check '''Trace On''' option.
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|| 10:48
|| In '''Algebra''' view, scroll down and double click on '''F'''.
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|| 10:54
|| Delete '''co-ordinates''' of '''F'''.
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|| 10:58
|| Select '''symbol alpha''', click on the letter '''alpha'''.

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|| 11:03
|| Insert '''alpha''' as '''x co-ordinate''' of '''F'''.
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|| 11:07
|| Type '''TANGENT''' as '''y co-ordinate''' of '''F''', and press '''Enter'''.
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|| 11:13
|| '''F''' has been changed to '''alpha comma TANGENT'''.
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|| 11:18
|| Point '''F''' will trace the '''tangent function''' graph as '''alpha''' value changes.
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|| 11:24
|| Increase '''alpha''' on the '''slider''' from 0 to 360 '''degrees''' 2 '''pi radians'''.
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|| 11:32
|| '''F''' increases from '''origin''' to '''infinity'''.

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|| 11:37
|| Note '''vertical asymptote''' at '''pi''' divided by 2 '''radians'''.
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|| 11:42
|| '''Tangent''' value is plus '''infinity''' at '''pi''' divided by 2 '''radians'''.

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|| 11:49
|| It is minus '''infinity''' at 3 '''pi''' divided by 2 '''radians'''.
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|| 11:55
|| In '''input bar''', type '''f x in parentheses is equal to tan x in parentheses''' and press '''Enter'''.
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|| 12:07
|| The '''tangent function''' is graphed beyond minus 2 '''pi''' and plus 2 '''pi radians'''.
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|| 12:16
|| Click on and move '''Graphics''' view to see graph of '''f of x''' beyond '''minus''' 2 '''pi''' and '''plus''' 2 '''pi radians'''.
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|| 12:28
|| Click on and move '''Graphics''' view to see '''plus 2''' '''pi radians''' along '''x axis'''.
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||12:37
|| Drag '''slider alpha''' back to 0 '''degrees''' to see traces of '''F'''.
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|| 12:43
|| Also compare the '''tangent function f of x''' with traces of '''F'''.
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||12:50
|| Let us summarize.
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|| 12:52
|| In this tutorial, we have learnt

how to use '''GeoGebra''' to calculate and graph '''sin alpha''', '''cos alpha''' and '''tan alpha'''
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|| 13:03
|| Assignment

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

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

angles whose sum is 180 '''degrees'''.

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|| 13:21
|| Analyze the link between '''sine''' and '''cosine''' values for '''supplementary angles'''.
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|| 13:27
|| The video at the following link summarizes the '''Spoken Tutorial Project'''.

Please download and watch it.
|-
|| 13:35
|| The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.

For more details, please write to us.
|-
|| 13:44
|| Please post your timed queries on this forum.
|-
||13:48
|| '''Spoken Tutorial Project''' is funded by '''NMEICT, MHRD''', Government of India.

More information on this mission is available at this link.
|-
||14:01
|| This is '''Vidhya Iyer''' from '''IIT Bombay''' signing off.

Thank you for joining.
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|}