PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'''. |- ||00:07 ||In this tutorial, we w..."

2018-10-31T09:10:31Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'''. |- ||00:07 ||In this tutorial, we w..."

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

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||00:01
||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'''.

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||00:07
||In this tutorial, we will demonstrate '''Trig Tour''', an '''interactive PhET simulation'''.

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||00:15
||Here I am using, '''Ubuntu Linux OS''' version 16.04

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||00:22
||'''Java''' version 1.8.0

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||00:26
||'''Firefox Web Browser''' version 60.0.2

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||00:32
||Learners should be familiar with trigonometry.

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||00:36
||Using this '''simulation''' we will learn how to,

Construct right triangles for a point moving around a unit circle

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||00:47
||Calculate trigonometric ratios, '''cos''', '''sin''' and '''tan''', of angle '''theta'''

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||00:54
||Graph '''theta''' versus '''cos''', '''sin''' and '''tan functions''' of '''theta''' along '''x''' and '''y axes'''

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||01:01
||Let us begin.

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||01:03
||Use the given link to download the '''simulation'''.

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||01:08
||I have already downloaded the '''Trig Tour simulation''' to my '''Downloads folder'''.

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||01:14
||To open the '''simulation''', right click on the '''trig-tour html''' file.

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||01:20
||Select the '''Open With Firefox Web Browser''' option.

The file opens in the '''browser'''.

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||01:29
||This is the '''interface''' for the '''Trig Tour''' simulation.

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||01:34
||The '''interface''' has four boxes:

'''Values'''

'''Unit circle'''

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||01:41
||'''Functions''', '''Special angles''', '''labels''' and '''grid'''

'''Graph'''

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||01:48
||The '''reset button''' takes you back to the starting point.

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||01:53
||In the '''Functions''' box, check '''Special angles, Labels, Grid''' and click '''cos'''.

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||02:05
||'''Cosine function'''

'''Cosine''' of an angle is the ratio of the lengths of the adjacent side to the hypotenuse.

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||02:15
||'''Cosine''' value is the '''x co-ordinate''' of a point moving around a unit circle.

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||02:23
||The center of this unit circle is the origin '''0 comma 0'''.

'''cosine theta''' is '''x''' divided by radius and hence, is '''x''' for the unit circle.

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||02:38
||A unit circle is drawn in a '''Cartesian coordinate system''' with '''x''' and '''y axes''' in the '''Unit Circle''' box.

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||02:49
||A red point is seen at the circumference of the circle on the '''x-axis'''.

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||02:55
||A blue arrow is seen along the '''x-axis''' pointing to the red point.

This corresponds to a radius of 1 for the unit circle.

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||03:07
||The '''Values''' box contains important values.

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||03:12
||The '''angle ϴ''' (theta) can be given in '''degrees''' or '''radians'''.

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||03:17
||Click the '''degrees''' radio button.

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||03:20
||'''x comma y''' are '''co-ordinates 1 comma 0''' of the red point at angle theta equals 0 degrees.

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||03:30
||When angle '''theta''' equals 0 degrees, '''x co-ordinate''' of the red point is 1.

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||03:38
|| '''x-axis''' of the graph shows angle '''theta'''.

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||03:43
||'''y-axis''' of the graph shows the amplitude of the '''cos theta''' function.

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||03:49
||At an angle '''theta''' of 0 degrees, '''cos theta''' is 1.

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||03:54
||The red point is at the highest amplitude of 1.

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||03:59
||In the '''Values''' box, click the '''radians radio button'''.

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||04:04
||x axis of the '''theta''' vs '''cos theta''' graph is converted into '''radians'''.

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||04:11
||Remember that '''pi radians''' are equal to '''180 degrees'''.

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||04:17
||One full rotation of 360 degrees is equal to 2 '''pi radians'''.

Again, click the '''degrees''' radio button.

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||04:29
||You can see empty circles on the unit circle.

In the '''Functions''' box, uncheck '''Special Angles'''.

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||04:39
||Observe how the empty circles disappear.

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||04:43
||Again, check '''Special Angles'''.

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||04:47
||These circles are angles made by the red point with the '''x-axis''' as it moves along the circle.

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||04:56
||Important angles have been chosen as '''Special angles'''.

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||05:01
||In the '''Unit Circle''', drag the red point counter-clockwise (CCW) to the next '''special angle'''.

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||05:09
||The red point has moved 30 degrees in the counter-clockwise direction along the circle.

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||05:16
||In the '''Values''' box, '''x comma y''' is the squareroot of 3 divided by 2 comma half.

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||05:25
||In the unit circle, according to '''Pythagoras’ theorem''', '''x squared''' plus '''y squared''' is 1.

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||05:34
||Two square lengths in the '''Cartesian plane''' is equal to 1 as radius of unit circle is 1.

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||05:44
||'''y''' covers only 1 square length and hence, is half.

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||05:50
||'''x''' covers 1 full and almost three-fourths of a second square.

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||05:57
||The squareroot of 3 divided by 2 is 0.866.

This is the value of '''x'''.
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|| 06:07
||Look at the graph.

The red point has moved to 30 degrees along the '''cos function'''.

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||06:15
||In the '''Values''' box, click '''radians''' radio button.

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||06:20
||This converts 30 degrees into '''pi''' divided by 6 radians for '''theta''' in the '''Values''' box.

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||06:29
||'''Sine function'''

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

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||06:39
||'''Sine''' value is the '''y-co-ordinate''' of the point moving around the same unit circle.

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||06:47
||'''Sine theta''' is '''y''' divided by radius and hence, is '''y''' for the unit circle.

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||06:56
||Drag the red point back to the x axis.

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||07:00
||In the '''Functions''' box, click '''sin'''.

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||07:04
||Click the '''degrees''' radio button.

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||07:07
||As seen earlier, '''x comma y''' are '''1 comma 0'''.

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||07:13
||Note the definitions of '''sine theta''' given earlier.

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||07:18
||When '''angle theta''' is 0 '''degrees''', the '''y co-ordinate''' of the red point is 0.

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||07:25
||The graph shows '''angle theta''' on the '''x-axis''' and the amplitude of the '''sine theta function''' on the '''y-axis'''.

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||07:34
||At '''angle theta''' of 0 '''degrees''', as '''sine theta''' is 0, the red point has amplitude 0.

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||07:43
||In the '''Unit Circle,''' drag the red point counter clockwise to the next '''special angle''' 30 '''degrees'''.

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||07:51
||In the '''Values''' box, note that '''x comma y''' is squareroot of 3 divided by 2 comma half.

Remember how you can calculate these.

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|| 08:04
||In the graph, the red point has moved to 30 '''degrees''' along the '''sine function'''.

Its amplitude is 0.5 or half.

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||08:17
||'''Tangent function'''

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

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||08:27
||'''Tan theta''' is the ratio of '''sin theta''' to '''cos theta''' and to '''y''' divided by '''x'''.

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||08:35
||Drag the red point back to the '''x-axis''' that is to '''1 comma 0'''.

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||08:44
||In the '''Functions''' box, click '''tan'''.

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||08:48
||When angle '''theta''' 0, '''tan theta''' is ratio of the '''y co-ordinate''' 0 to '''x co-ordinate''' 1 that is 0.

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||09:00
||The graph shows angle '''theta''' on the '''x-axis''' and the amplitude of the '''tan theta function''' on the '''y-axis'''.

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||09:09
||At '''angle theta''' 0, as '''tan theta''' is 0, the red point has amplitude of 0.

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||09:17
|| In the '''Unit Circle''', drag the red point counter clockwise to the '''special angle''' 90 '''degrees''' on the '''y-axis'''.

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||09:27
||In the '''Values''' box, '''x comma y''' has become '''0 comma 1'''.

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||09:33
||Note that '''tan theta''' is '''plus or minus infinity''' in the '''Values''' box.

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||09:40
||Now look at the graph.

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||09:43
||The red point has moved to 90 degrees where '''tan theta''' now falls on the vertical dotted line.

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||09:53
||This dotted line is the '''vertical asymptote''' of the '''function'''.

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||09:58
||It represents the value of '''x''' which the '''function''' approaches but never touches.

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||10:05
||Here, the '''function''' increases without bound towards '''infinity''' in both directions.

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||10:13
||Let us summarize.

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||10:16
||In this tutorial, we have demonstrated how to use the '''Trig Tour Phet simulation'''.

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||10:23
||Using this '''simulation''', we have learnt to:

Construct right triangles for a point moving around a unit circle

|-
||10:33
||Calculate trigonometric ratios, '''cos''', '''sin''' and '''tan''', of angle '''theta'''

|-
||10:39
||Graph '''theta''' versus '''cos''', '''sin''' and '''tan functions''' of '''theta''' along '''x''' and '''y axes'''.

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||10:46
||As an '''assignment''', observe: '''Cosine, sine '''and''' tangent''' values for all '''special angles'''

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||10:53
||'''Cosine, sin''' and '''tangent''' graphs.

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||10:57
||Relationship between ratios for supplementary angles

The sum of supplementary angles is 180 degrees.

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||11:08
||The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it

|-
||11:17
||The '''Spoken Tutorial Project '''team conducts workshops using spoken tutorials and gives certificates on passing online tests.

For more details, please write to us.

|-
||11:29
||Please post your timed queries in this forum.

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||11:33
||This project is partially funded by '''Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching'''.

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||11:42
||'''Spoken Tutorial Project''' is funded by '''NMEICT''', '''MHRD''', Government of India.

More information on this mission is available at this link.

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||11:55
||This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.

Thank you for joining.
|-
|}

PhET/C2/Trig-tour/English-timed - Revision history

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'''. |- ||00:07 ||In this tutorial, we w..."