PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Inverse Trigonometric Functions'''. |- ||00:06 ||In this '''tutorial''', we will learn..."

2020-10-21T07:18:58Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Inverse Trigonometric Functions'''. |- ||00:06 ||In this '''tutorial''', we will learn..."

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{|border=1
||'''Time'''
||'''Narration'''

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||00:01
||Welcome to this tutorial on '''Inverse Trigonometric Functions'''.

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||00:06
||In this '''tutorial''', we will learn to use '''GeoGebra''' to

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||00:11
||Plot graphs of '''inverse trigonometric functions'''

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||00:15
||Compare them to graphs of '''trigonometric functions'''

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||00:19
||Create '''check-boxes''' to group and show or hide '''functions'''

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||00:24
||To follow this '''tutorial''', you should be familiar with:

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||00:28
||'''GeoGebra''' interface

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||00:31
||'''Trigonometry'''

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||00:33
||For relevant '''tutorials''', please visit our website.
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||00:37
||Here I am using:

'''Ubuntu Linux OS version 14.04'''

'''GeoGebra 5.0.388.0 hyphen d'''
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||00:51
||I have already opened the '''GeoGebra''' interface.
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||00:56
||Now let us change '''x Axis units''' to '''radians'''.

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||01:01
||In '''Graphics''' view, double-click on the '''x axis''' and then on '''Object Properties'''.
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||01:08
||In the '''Object Properties''' menu, click on '''Preferences Graphics''' and then on '''xAxis'''.
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||01:17
||Check the '''Distance''' option, select '''pi''' divided by 2 and then the '''Ticks first option'''.
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||01:28
||Close the''' Preferences''' box.
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||01:31
||Units of '''x-axis''' are in '''radians''' with interval of '''pi''' divided by 2 as shown.

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||01:38
||'''GeoGebra''' will convert '''degrees''' of angle '''alpha''' to '''radians'''.
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||01:44
||Note that the name appears when you place the mouse over any '''tool icon''' in the '''toolbar'''.
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||01:52
||In the '''Graphics toolbar''', click on '''Slider''' and then in the top of '''Graphics''' view.
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||02:01
||A '''slider dialog-box''' appears.
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||02:04
||By default, '''Number''' radio button is selected.
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||02:08
||In the '''Name''' field, select '''theta''' from the '''Symbol menu'''.
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||02:14
||Type the '''Min''' value as minus 360 and '''Max''' plus 360 with '''Increment''' 1.

Click '''OK'''.
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||02:27
||This creates a '''number slider theta''' from minus 360 to plus 360.
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||02:34
||In the '''input bar''', type '''alpha is equal to theta divided by 180 in parentheses''', and then '''pi'''.

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||02:47
||Note how '''GeoGebra''' inserts a space between the right parenthesis and '''pi''' for multiplication.

Press '''Enter'''.
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||02:57
||Drag '''slider theta''' to minus 360 and then back to 360.
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||03:04
||In '''Algebra''' view, observe how '''alpha''' changes from minus '''2pi''' to '''2pi radians''' as you change '''theta'''.
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||03:13
||Drag '''slider theta''' back to minus 360.
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||03:18
||In the '''input bar''', type the following command:

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||03:22
||'''f underscore S colon is equal to Function with capital F'''

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||03:29
||Type the following words in square brackets.

'''sin, x in parentheses, comma minus 2 pi comma alpha'''.

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||03:42
||Press '''Enter'''.
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||03:44
||Drag the boundary to see '''Algebra''' view properly.
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|| 03:49
||Here, '''fS''' defines the '''sine function''' of '''x'''.

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||03:54
||'''x''' is between '''-2 pi''' and '''alpha''' which can take a maximum value of '''2pi'''.

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||04:03
||This is called the '''domain''' of the '''function'''.
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||04:08
||Drag the boundary to see '''Graphics''' View properly.
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|| 04:13
||Drag '''slider theta''' from minus 360 to 360.
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||04:19
||This graphs the '''sine function''' of '''x'''.
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||04:23
||In the toolbar, click on the bottom right triangle of the last button.

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||04:29
||Note that this button is called '''Move Graphics View'''.
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||04:34
||In the menu that appears, click on '''Zoom Out'''.

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||04:39
||Click in '''Graphics view''' to see '''2 pi radians''' on either side of the '''origin'''.
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|| 04:47
||Again, click on '''Move Graphics View''' and drag the background to see the graph properly.
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||04:56
||Drag '''slider theta''' back to minus 360.
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||05:01
||'''Inverse Trigonometric Functions'''

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||05:04
||For example, If '''inverse sine''' of '''z''' also known as '''arcsin''' of '''z''' is '''w'''.

Then, '''z''' is '''sin w'''.

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||05:15
||'''w''' can have multiple values.

So a '''principal value''' has to be defined and the '''domain''' has to be restricted.

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||05:23
||To get the '''inverse function''' graph, interchange '''x''' and '''y''' axes.

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||05:29
||Next, change curvature of '''trigonometric function graph'''.

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||05:34
||You can pause and refer to the example in the '''additional material''' provided for this '''tutorial'''.

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||05:41
||Let us go back to the '''GeoGebra''' window.

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||05:45
||In the '''input bar''', type the following command:

'''i underscore S colon is equal to Function with capital F'''

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||05:56
||Type the following words in square brackets.

'''a sin, x in parentheses, comma minus 1 comma 1'''

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||06:06
||Press '''Enter'''.

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||06:08
||Drag the boundary to see '''Algebra''' view properly.

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||06:12
||This graphs the '''inverse sine''' (or '''arc sine''') function of '''x'''.

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||06:18
||Note that '''x''' and '''y axes''' are interchanged for this '''inverse sine function'''.

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||06:25
||Its '''domain''' set of '''x''' values lies between minus 1 and 1.

Observe the graph.
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|| 06:34
||Drag the boundary to see '''Graphics''' view properly.
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||06:39
||In the '''input bar''', type the following command:

'''P underscore S colon is equal to''' Type the following words in parentheses '''sin alpha in parentheses comma alpha'''. Press '''Enter'''.

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||06:58
||This creates point '''PS''' on the '''inverse sine''' graph.

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||07:04
||On the '''sine function''' graph, '''PS''' would be '''alpha comma sine alpha'''.
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||07:10
||In '''Algebra''' view, right-click on '''PS''', check the '''Trace On''' option.
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||07:17
||Drag '''slider theta''' to 360.
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||07:21
||Traces appear for the '''inverse sine function''' graph for '''alpha'''.

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||07:26s
||'''fs''' also appears in '''Graphics''' view.

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||07:30
||Compare '''iS''' and traces of '''PS'''.

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||07:35
||Note that the '''domain''' for the graph that '''PS''' traces is not restricted from minus 1 to 1.
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||07:43
||Drag '''slider theta''' back to minus 360.
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||07:47
||Click and drag the background in '''Graphics''' view to erase traces of '''PS'''.
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||07:53
||In '''Algebra''' view, uncheck '''fS,''' '''iS''', and '''PS''' to hide them.

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||08:02
||'''Cosine and Inverse Cosine Functions'''

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||08:06
||Follow the steps shown for '''SINE''' to graph the '''cosine function fC'''.

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||08:12
||Its '''domain''' should be from '''minus 2 pi''' to '''alpha'''.

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||08:17
||Graph the '''inverse cosine function iC" in the '''domain''' from minus 1 to 1.

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||08:24
||Create a point '''PC''' whose '''co-ordinates''' are '''cos alpha comma alpha'''.

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||08:30
||The '''domain''' of the inverse cosine''' graph that '''PC''' traces will go beyond minus 1 and 1.
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||08:37
||The '''cosine''' and '''inverse cosine functions''' should look like this.
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||08:46
||In '''Algebra view, uncheck '''fC, iC and PC and move the background to erase traces of PC.
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||08:58
||Drag '''slider theta''' back to minus 360.
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||09:03
||'''Tangent and Inverse Tangent Functions'''

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||09:07
||Now graph the '''tangent function fT'''.

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||09:11
||Its domain should also be from '''minus 2 pi''' to '''alpha'''.

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||09:16
||We will look at the graph for the '''inverse tangent function iT'''.

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||09:21
||Its domain will be from minus infinity to infinity.

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||09:26
||Create a point '''PT''' whose '''co-ordinates''' are '''tan alpha comma alpha'''.

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||09:32
||The '''domain''' of the '''inverse tangent''' graph that '''PT''' traces will go beyond minus 1 and 1.
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||09:39
||Let us look at the '''inverse tangent function''' graph in the domain from minus 1 to 1.
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||09:45
||To type infinity, click in the '''input bar''' and on '''symbol alpha''' appearing at the right end of the bar.

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||09:53
||In the '''symbol menu''', click on the '''infinity symbol''' in the third row and third column from the right.

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||10:01
||In the '''input bar''', type the following command:

'''i underscore T colon is equal to Function with capital F'''

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||10:12
||Type the following words in square brackets '''atan, x in parentheses, comma minus infinity comma infinity'''. Press '''Enter'''.
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||10:26
||This graphs the '''inverse tangent''' function of '''x'''.

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||10:31
||'''x''' lies between minus '''infinity''' and '''infinity'''.

Observe the graph.
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||10:39
||Drag '''slider theta''' to 360.
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||10:43
||Compare traces of '''PT''' and '''iT'''.
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||10:48
||Drag '''slider theta''' back to minus 360.
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||10:53
||Drag the background slightly to the erase the traces of '''PT'''
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||10:58
||In '''Algebra''' view, uncheck '''fT''' and '''PT'''.
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||11:04
||In '''Algebra''' view, check '''fS''', '''iS''', and '''PS''' to show them again.
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||11:14
||Let us create check boxes to make it easier to group and see different functions at a time.
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||11:21
||Under '''Slider''', click on '''Check-box'''.

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||11:25
||Click on the top of the grid in '''Graphics''' view.
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||11:29
||A'''Check-Box to Show/Hide Objects dialog-box''' appears.
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||11:35
||In the '''Caption''' field, type '''SIN.'''
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||11:38
||Click on '''Objects''' drop-down menu to select '''fS, iS''' and '''PS''', one by one, click '''Apply'''.
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||11:50
||A '''check-box''' '''SIN''' is created in '''Graphics''' view.

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||11:55
||It gives us the option to display or hide '''sine, arcsine''' graphs and point '''PS'''.
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||12:02
||Again, click on '''Check Box'''.

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||12:05
||Click on the top of the grid in '''Graphics''' view.
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||12:09
||A '''Checkbox to Show/Hide Objects''' dialog-box appears.
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||12:14
||In the '''Caption''' field, type '''TAN'''.
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||12:16
||Click on '''Objects''' drop-down menu to select '''fT, iT''' and '''PT''', one by one, click '''Apply'''.
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||12:29
||A '''checkbox''' '''TAN''' is created in '''Graphics''' view.

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||12:33
||It gives us the option to display or hide '''tangent, arctangent''' graphs and point '''PT'''.
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||12:40
||In the '''toolbar''', click on the first '''Move''' button and uncheck all boxes.
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||12:48
||Check the '''SIN''' box.
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||12:51
||Drag '''slider theta''' to 360.
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||12:55
||Observe '''fS, iS''' and traces of '''PS''' appear in '''Graphics''' view.
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||13:03
||Uncheck the '''SIN''' box.
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||13:06
||Click on and move '''Graphics''' view slightly to erase traces of '''PS'''.
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||13:12
||Drag '''slider theta''' back to minus 360.
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||13:17
||Check the '''TAN''' box.
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||13:19
||Drag '''slider theta''' to 360.
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||13:23
||Observe '''fT, iT''' and traces of '''PT''' appear in '''Graphics''' view.
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||13:31
||Drag '''slider theta''' back to minus 360.
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||13:35
||Check the '''SIN''' box.
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||13:37
||Drag '''slider theta''' to 360.
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||13:41
||Observe the '''functions''' appearing in '''Graphics''' view.
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||13:45
||Let us summarize.
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||13:47
||In this '''tutorial''', we have learnt how to use '''GeoGebra''' to:

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||13:52
||Graph '''trigonometric functions'''

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||13:54
||Graph '''inverse trigonometric functions'''

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||13:57
||Create '''checkboxes''' to group and show/hide '''functions'''
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||14:02
||As an assignment,

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||14:04
||Plot graphs of, '''Secant''' and '''arcsecant''', '''Cosecant''' and '''arccosecant''', '''Cotangent''' and '''arccotangent'''

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||14:17
||For hints, you can refer to the '''additional material''' provided.
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||14:22
||The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it.
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||14:30
||The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.

For more details, please write to us.
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||14:40
||Please post your timed queries on this forum.
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||14:44
||The '''Spoken Tutorial Project''' is funded by '''NMEICT, MHRD''', Government of India.

More information on this mission is available at this link.
|-
||14:56
||This is '''Vidhya Iyer''' from '''IIT Bombay,''' signing off.

Thank you for joining.
|-
|}

Applications-of-GeoGebra/C2/Inverse-Trigonometric-Functions/English-timed - Revision history

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Inverse Trigonometric Functions'''. |- ||00:06 ||In this '''tutorial''', we will learn..."