Difference between revisions of "PhET/C2/Trig-tour/English"

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(Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''Trig Tour''', an '''interactive PhE...")
 
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{|border=1
 
{|border=1
−
| | '''Visual Cue'''
+
||'''Visual Cue'''
−
| | '''Narration'''
+
||'''Narration'''
  
 
|-
 
|-
−
| | '''Slide Number 1'''
+
||'''Slide Number 1'''
  
 
'''Title Slide'''
 
'''Title Slide'''
−
| | Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'''.
+
||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'''.
 
|-
 
|-
−
| | '''Slide Number 2'''
+
||'''Slide Number 2'''
  
 
'''Learning Objectives'''
 
'''Learning Objectives'''
Line 21: Line 16:
  
 
'''Trig Tour PhET simulation'''
 
'''Trig Tour PhET simulation'''
−
| | In this tutorial, we will demonstrate '''Trig Tour''', an '''interactive PhET simulation'''.
+
||In this tutorial, we will demonstrate '''Trig Tour''', an '''interactive PhET simulation'''.
 
|-
 
|-
−
| | '''Slide Number 3'''
+
||'''Slide Number 3'''
  
 
'''System Requirements'''
 
'''System Requirements'''
Line 32: Line 27:
  
 
'''Firefox Web Browser''' v 60.0.2
 
'''Firefox Web Browser''' v 60.0.2
−
| | Here I am using,
+
||Here I am using,
  
 
'''Ubuntu Linux OS''' version 16.04
 
'''Ubuntu Linux OS''' version 16.04
Line 40: Line 35:
 
'''Firefox Web Browser''' version 60.0.2
 
'''Firefox Web Browser''' version 60.0.2
 
|-
 
|-
−
| | '''Slide Number 4'''
+
||'''Slide Number 4'''
  
 
'''Pre-requisites'''
 
'''Pre-requisites'''
−
| | Learners should be familiar with trigonometry.
+
||Learners should be familiar with trigonometry.
 
|-
 
|-
−
| | '''Slide Number 5'''
+
||'''Slide Number 5'''
  
 
'''Learning Goals'''
 
'''Learning Goals'''
Line 51: Line 46:
 
Construct right triangles for a point moving around a unit circle
 
Construct right triangles for a point moving around a unit circle
  
−
Calculate trigonometric ratios, '''''cos, sin''''' and '''''tan''''', of angle '''ϴ''' (theta)
+
Calculate '''trigonometric ratios''', '''cos''', '''sin''' and '''tan''', of angle '''ϴ''' (theta)
  
−
Graph ϴ versus '''''cos, sin''''' and '''''tan'' '''functions''' of '''ϴ''' along '''x''' and '''y axes'''
+
Graph ϴ versus '''cos''', '''sin''' and '''tan''' '''functions''' of '''ϴ''' along '''x''' and '''y axes'''
−
| |  
+
||Using this '''simulation''' we will learn how to,
−
Using this '''simulation''' we will learn how to,
+
  
 
Construct right triangles for a point moving around a unit circle
 
Construct right triangles for a point moving around a unit circle
  
−
Calculate trigonometric ratios, '''''cos, sin''''' and '''''tan''''', of angle theta
+
Calculate trigonometric ratios, '''cos''', '''sin''' and '''tan''', of angle '''theta'''
  
−
Graph '''theta''' versus '''''cos, sin''''' and '''''tan''''' '''functions''' of '''theta''' along '''x''' and '''y axes'''
+
Graph '''theta''' versus '''cos''', '''sin''' and '''tan functions''' of '''theta''' along '''x''' and '''y axes'''
 
|-
 
|-
−
| |  
+
||
−
| | Let us begin.
+
||Let us begin.
 
|-
 
|-
−
| | '''Slide Number 6'''
+
||'''Slide Number 6'''
  
 
'''Link for PhET simulation'''
 
'''Link for PhET simulation'''
Line 72: Line 66:
  
 
[http://phet.colorado.edu/ http://phet.colorado.edu]
 
[http://phet.colorado.edu/ http://phet.colorado.edu]
−
| | Use the given link to download the '''simulation'''.
+
||Use the given link to download the '''simulation'''.
  
 
[http://phet.colorado.edu/ http://phet.colorado.edu]
 
[http://phet.colorado.edu/ http://phet.colorado.edu]
 
|-
 
|-
−
| | Point to the file in '''Downloads folder'''.
+
||Point to the file in '''Downloads folder'''.
−
| | I have already downloaded the '''Trig Tour simulation''' to my '''Downloads folder'''.
+
||I have already downloaded the '''Trig Tour simulation''' to my '''Downloads folder'''.
 
|-
 
|-
−
| | Right click on '''trig-tour_en.html''' file.
+
||Right click on '''trig-tour_en.html''' file.
  
 
Select '''Open With Firefox Web Browser''' option.
 
Select '''Open With Firefox Web Browser''' option.
  
 
Point to the '''browser''' address.
 
Point to the '''browser''' address.
−
| | To open the '''simulation''', right click on the '''trig-tour_en.html''' file.
+
||To open the '''simulation''', right click on the '''trig-tour_en.html''' file.
  
 
Select the '''Open With Firefox Web Browser''' option.
 
Select the '''Open With Firefox Web Browser''' option.
Line 90: Line 84:
 
The file opens in the '''browser'''.
 
The file opens in the '''browser'''.
 
|-
 
|-
−
| | '''Cursor''' on the '''interface'''.
+
||'''Cursor''' on the '''interface'''.
−
| | This is the '''interface''' for the '''Trig Tour''' simulation.
+
||This is the '''interface''' for the '''Trig Tour''' simulation.
 
|-
 
|-
−
| | Point to each box in the '''interface'''.
+
||Point to each box in the '''interface'''.
  
 
Point to the '''reset button'''.
 
Point to the '''reset button'''.
−
| | The '''interface''' has four boxes:
+
||The '''interface''' has four boxes:
  
 
'''Values'''
 
'''Values'''
Line 102: Line 96:
 
'''Unit circle'''
 
'''Unit circle'''
  
−
'''Functions, special angles, labels and grid'''
+
'''Functions''', '''Special angles''', '''labels''' and '''grid'''
  
 
'''Graph'''
 
'''Graph'''
Line 108: Line 102:
 
The '''reset button''' takes you back to the starting point.  
 
The '''reset button''' takes you back to the starting point.  
 
|-
 
|-
−
| | Check '''Special angles, Labels''' and '''Grid''' in '''Functions''' box.  
+
||Check '''Special angles''', '''Labels''' and '''Grid''' in '''Functions''' box.  
−
| | In the '''Functions '''box,''' check '''Special angles, Labels, Grid''' and click '''cos'''.
+
||In the '''Functions''' box, check '''Special angles, Labels, Grid''' and click '''cos'''.
 
|-
 
|-
−
| | '''Slide Number 7'''
+
||'''Slide Number 7'''
  
 
'''Cosine function'''
 
'''Cosine function'''
Line 122: Line 116:
  
 
'''cos(ϴ)''' = '''x'''/'''radius''' = '''x/1'''
 
'''cos(ϴ)''' = '''x'''/'''radius''' = '''x/1'''
−
| |  
+
||'''Cosine''' of an angle is the ratio of the lengths of the adjacent side to the hypotenuse.
−
 
+
−
'''Cosine''' of an angle is the ratio of the lengths of the adjacent side to the hypotenuse.
+
  
 
'''Cosine''' value is the '''x co-ordinate''' of a point moving around a unit circle.
 
'''Cosine''' value is the '''x co-ordinate''' of a point moving around a unit circle.
Line 130: Line 122:
 
The center of this unit circle is the origin '''0 comma 0'''.
 
The center of this unit circle is the origin '''0 comma 0'''.
  
−
'''cosin theta''' is '''x''' divided by radius and hence, is '''x''' for the unit circle.
+
'''cosine theta''' is '''x''' divided by radius and hence, is '''x''' for the unit circle.
 
|-
 
|-
−
| | Point to the '''Unit Circle''' box.
+
||Point to the '''Unit Circle''' box.
−
| | A unit circle is drawn in a '''Cartesian coordinate system''' with '''x''' and '''y axes''' in the '''Unit Circle''' box.
+
||A unit circle is drawn in a '''Cartesian coordinate system''' with '''x''' and '''y axes''' in the '''Unit Circle''' box.
 
|-
 
|-
−
| | Point to the red point.  
+
||Point to the red point.  
  
 
Point to the blue arrow.  
 
Point to the blue arrow.  
−
| | A red point is seen at the circumference of the circle on the '''x-axis'''.
+
||A red point is seen at the circumference of the circle on the '''x-axis'''.
  
 
A blue arrow is seen along the '''x-axis''' pointing to the red point.  
 
A blue arrow is seen along the '''x-axis''' pointing to the red point.  
Line 144: Line 136:
 
This corresponds to a radius of 1 for the unit circle.  
 
This corresponds to a radius of 1 for the unit circle.  
 
|-
 
|-
−
| | Point to the '''Values''' box.
+
||Point to the '''Values''' box.
−
| | The '''Values''' box contains important values.  
+
||The '''Values''' box contains important values.  
 
|-
 
|-
−
| | Point to the '''degrees''' and '''radians radio buttons'''.
+
||Point to the '''degrees''' and '''radians''' radio buttons.
−
| | The '''angle ϴ''' (theta) can be given in '''degrees''' or '''radians'''.
+
||The '''angle ϴ''' (theta) can be given in '''degrees''' or '''radians'''.
 
|-
 
|-
−
| | Check '''degrees radio button'''.  
+
||Check '''degrees''' radio button.  
−
| | Click the '''degrees radio button'''.  
+
||Click the '''degrees''' radio button.  
 
|-
 
|-
−
| | Point to '''(x,y) = (1,0)''' and '''angle = 0º''' in the '''Values box'''.  
+
||Point to '''(x,y) = (1,0)''' and '''angle = 0º''' in the '''Values box'''.  
  
  
 
Point to the red point in '''Unit Circle''' box.  
 
Point to the red point in '''Unit Circle''' box.  
−
| | '''x comma y''' are '''co-ordinates 1 comma 0''' of the red point at '''angle theta equals''' 0 degrees .
+
||'''x comma y''' are '''co-ordinates 1 comma 0''' of the red point at angle theta equals 0 degrees.
 
|-
 
|-
−
| | Point to '''cosϴ = x/1 = 1''' in '''Values''' box.
+
||Point to '''cosϴ = x/1 = 1''' in '''Values''' box.
−
| | When '''angle theta equals''' 0 '''degrees''', '''x co-ordinate''' of the red point is 1.  
+
||When angle '''theta''' equals 0 degrees, '''x co-ordinate''' of the red point is 1.  
 
|-
 
|-
−
| | Point to the red point in the '''Graph''' box.
+
||Point to the red point in the '''Graph''' box.
−
| | '''x-axis''' of the graph shows '''angle theta'''.
+
|| '''x-axis''' of the graph shows angle '''theta'''.
  
 
'''y-axis''' of the graph shows the amplitude of the '''cos theta''' function.  
 
'''y-axis''' of the graph shows the amplitude of the '''cos theta''' function.  
  
−
At an '''angle theta''' of 0 '''degrees''', '''cos theta''' is 1.  
+
At an angle '''theta''' of 0 degrees, '''cos theta''' is 1.  
  
 
The red point is at the highest amplitude of 1.  
 
The red point is at the highest amplitude of 1.  
 
|-
 
|-
−
| | Check '''degrees radio button'''.  
+
||Check '''degrees radio button'''.  
−
| | In the '''Values''' box, click the '''radians radio button'''.  
+
||In the '''Values''' box, click the '''radians radio button'''.  
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | x axis of the '''theta''' vs '''cos theta''' graph is converted into '''radians'''.  
+
||x axis of the '''theta''' vs '''cos theta''' graph is converted into '''radians'''.  
  
 
Remember that '''pi radians''' are equal to '''180 degrees'''.
 
Remember that '''pi radians''' are equal to '''180 degrees'''.
  
−
One full rotation of 360 '''degrees''' is equal to 2 '''pi radians'''.
+
One full rotation of 360 degrees is equal to 2 '''pi radians'''.
  
−
Again, click the '''degrees radio button'''.  
+
Again, click the '''degrees''' radio button.  
 
|-
 
|-
−
| | Point to the empty circles.  
+
||Point to the empty circles.  
  
 
In the '''Functions''' box, uncheck '''Special Angles'''.  
 
In the '''Functions''' box, uncheck '''Special Angles'''.  
  
−
| | You can see empty circles on the unit circle.  
+
||You can see empty circles on the unit circle.  
  
 
In the '''Functions''' box, uncheck '''Special Angles'''.  
 
In the '''Functions''' box, uncheck '''Special Angles'''.  
Line 193: Line 185:
 
Observe how the empty circles disappear.  
 
Observe how the empty circles disappear.  
 
|-
 
|-
−
| | Again, check '''Special Angles'''.  
+
||Check '''Special Angles'''.  
−
| | Again, check '''Special Angles'''.  
+
||Again, check '''Special Angles'''.  
 
|-
 
|-
−
| | Point to the '''Special Angles'''.  
+
||Point to the '''Special Angles'''.  
−
| | These circles are angles made by the red point with the '''x-axis''' as it moves along the circle.  
+
||These circles are angles made by the red point with the '''x-axis''' as it moves along the circle.  
  
−
Important angles have been chosen as '''Special Angles'''.  
+
Important angles have been chosen as '''Special angles'''.  
 
|-
 
|-
−
| | In the '''Unit Circle''', drag red point counter-clockwise (CCW) to the next '''special angle'''.
+
||In the '''Unit Circle''', drag red point counter-clockwise (CCW) to the next '''special angle'''.
  
 
Point to '''angle = 30º''' in '''Values''' box and to the red point in the '''Unit Circle''' box.  
 
Point to '''angle = 30º''' in '''Values''' box and to the red point in the '''Unit Circle''' box.  
−
| | In the '''Unit Circle''', drag the red point counter-clockwise (CCW) to the next '''special angle'''.  
+
||In the '''Unit Circle''', drag the red point counter-clockwise (CCW) to the next '''special angle'''.  
  
  
−
The red point has moved 30º in the counter-clockwise direction along the circle.  
+
The red point has moved 30 degrees in the counter-clockwise direction along the circle.  
 
|-
 
|-
−
| | Point to the '''Values''' box.  
+
||Point to the '''Values''' box.  
  
 
Point to the unit circle.  
 
Point to the unit circle.  
−
| | In the '''Values''' box, '''x comma y''' is the squareroot of 3 divided by 2 comma half.
+
||In the '''Values''' box, '''x comma y''' is the squareroot of 3 divided by 2 comma half.
  
 
In the unit circle, according to '''Pythagoras’ theorem''', '''x squared''' plus '''y squared''' is 1.  
 
In the unit circle, according to '''Pythagoras’ theorem''', '''x squared''' plus '''y squared''' is 1.  
 
|-
 
|-
−
| | Point to the unit circle.  
+
||Point to the unit circle.  
−
| | Two square lengths in the '''Cartesian plane''' is equal to 1 as radius of unit circle is 1.  
+
||Two square lengths in the '''Cartesian plane''' is equal to 1 as radius of unit circle is 1.  
  
 
'''y''' covers only 1 square length and hence, is half.
 
'''y''' covers only 1 square length and hence, is half.
Line 223: Line 215:
 
'''x''' covers 1 full and almost three-fourths of a second square.  
 
'''x''' covers 1 full and almost three-fourths of a second square.  
 
|-
 
|-
−
| | Point to the '''Values''' box.  
+
||Point to the '''Values''' box.  
−
| | The squareroot of 3 divided by 2 is 0.866.  
+
||The squareroot of 3 divided by 2 is 0.866.  
  
 
This is the value of '''x'''.  
 
This is the value of '''x'''.  
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | Look at the graph.  
+
||Look at the graph.  
  
 
The red point has moved to 30 degrees along the '''cos function'''.  
 
The red point has moved to 30 degrees along the '''cos function'''.  
 
|-
 
|-
−
| | Check '''radians radio button''' in the '''Values''' box.  
+
||Check '''radians''' radio button in the '''Values''' box.  
  
 
Point to the '''Values''' box and the Graph.  
 
Point to the '''Values''' box and the Graph.  
−
| | In the '''Values''' box, click '''radians radio button'''.  
+
||In the '''Values''' box, click '''radians''' radio button.  
  
 
This converts 30 degrees into '''pi''' divided by 6 radians for '''theta''' in the '''Values''' box.
 
This converts 30 degrees into '''pi''' divided by 6 radians for '''theta''' in the '''Values''' box.
 
|-
 
|-
−
| | '''Slide Number 8'''
+
||'''Slide Number 8'''
  
 
'''Sine function'''
 
'''Sine function'''
Line 249: Line 241:
  
 
'''sin(ϴ) = y/radius = y/1'''
 
'''sin(ϴ) = y/radius = y/1'''
−
| |  
+
||'''Sine function'''
−
 
+
−
'''Sine function'''
+
  
 
'''Sine''' of an angle is the ratio of the lengths of the opposite side to the hypotenuse.
 
'''Sine''' of an angle is the ratio of the lengths of the opposite side to the hypotenuse.
Line 258: Line 248:
  
  
−
'''Sin theta''' is '''y''' divided by radius and hence, is '''y''' for the unit circle.
+
'''Sine theta''' is '''y''' divided by radius and hence, is '''y''' for the unit circle.
 
|-
 
|-
−
| | Drag the red point back to the x axis.  
+
||Drag the red point back to the x axis.  
−
| | Drag the red point back to the x axis.  
+
||Drag the red point back to the x axis.  
 
|-
 
|-
−
| | In the '''Functions''' box, click '''sin'''.
+
||In the '''Functions''' box, click '''sin'''.
−
| | In the '''Functions''' box, click '''sin'''.
+
||In the '''Functions''' box, click '''sin'''.
 
|-
 
|-
−
| | Check '''degrees radio button'''.  
+
||Check '''degrees''' radio button.  
−
| | Click the '''degrees radio button'''.  
+
||Click the '''degrees''' radio button.  
 
|-
 
|-
−
| | Point to the '''Values''' box.
+
||Point to the '''Values''' box.
  
 
Point to the unit circle.  
 
Point to the unit circle.  
−
| | As seen earlier, '''x comma y''' are '''1 comma 0'''.
+
||As seen earlier, '''x comma y''' are '''1 comma 0'''.
  
−
Note the definitions of '''sin theta''' given earlier.  
+
Note the definitions of '''sine theta''' given earlier.  
  
 
When '''angle theta''' is 0 '''degrees''', the '''y co-ordinate''' of the red point is 0.
 
When '''angle theta''' is 0 '''degrees''', the '''y co-ordinate''' of the red point is 0.
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | The graph shows '''angle theta''' on the '''x-axis''' and the amplitude of the '''sin theta function''' on the '''y-axis'''.  
+
||The graph shows '''angle theta''' on the '''x-axis''' and the amplitude of the '''sine theta function''' on the '''y-axis'''.  
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | At '''angle theta''' of 0 '''degrees''', as '''sin theta''' is 0, the red point has amplitude 0.
+
||At '''angle theta''' of 0 '''degrees''', as '''sine theta''' is 0, the red point has amplitude 0.
 
|-
 
|-
−
| | In the '''Unit Circle,''' drag red point CCW to the next '''special angle''' 30 '''degrees'''.
+
||In the '''Unit Circle,''' drag red point CCW to the next '''special angle''' 30 '''degrees'''.
−
| | In the '''Unit Circle,''' drag the red point CCW to the next '''special angle''' 30 '''degrees'''.
+
||In the '''Unit Circle,''' drag the red point counter clockwise to the next '''special angle''' 30 '''degrees'''.
 
|-
 
|-
−
| | Point to the '''Values''' box.  
+
||Point to the '''Values''' box.  
−
| | In the '''Values''' box, note that '''x comma y''' is squareroot of 3 divided by 2 comma half.  
+
||In the '''Values''' box, note that '''x comma y''' is squareroot of 3 divided by 2 comma half.  
  
 
Remember how you can calculate these.  
 
Remember how you can calculate these.  
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | In the graph, the red point has moved to 30 '''degrees''' along the '''sine function'''.  
+
||In the graph, the red point has moved to 30 '''degrees''' along the '''sine function'''.  
  
 
Its amplitude is 0.5 or half.  
 
Its amplitude is 0.5 or half.  
 
|-
 
|-
−
| | '''Slide Number 9'''
+
||'''Slide Number 9'''
  
 
'''Tangent function'''
 
'''Tangent function'''
Line 304: Line 294:
  
 
'''tan(ϴ) = sinϴ/cosϴ = y/x'''
 
'''tan(ϴ) = sinϴ/cosϴ = y/x'''
−
| |  
+
||'''Tangent function'''
−
'''Tangent function'''
+
  
 
'''Tangent''' of an angle is the ratio of the lengths of opposite side to adjacent side.
 
'''Tangent''' of an angle is the ratio of the lengths of opposite side to adjacent side.
Line 312: Line 301:
 
'''Tan theta''' is the ratio of '''sin theta''' to '''cos theta''' and to '''y''' divided by '''x'''.
 
'''Tan theta''' is the ratio of '''sin theta''' to '''cos theta''' and to '''y''' divided by '''x'''.
 
|-
 
|-
−
| | Drag the red point back to the '''x-axis''', that is to (1,0).  
+
||Drag the red point back to the '''x-axis''', that is to (1,0).  
−
| | Drag the red point back to the '''x-axis''' that is to '''1 comma 0'''.  
+
||Drag the red point back to the '''x-axis''' that is to '''1 comma 0'''.  
 
|-
 
|-
−
| | Click '''tan''' in '''Functions''' box.
+
||Click '''tan''' in '''Functions''' box.
−
| | In the '''Functions''' box, click '''tan'''.
+
||In the '''Functions''' box, click '''tan'''.
 
|-
 
|-
−
| | Point to '''co-ordinates''' in '''Values''' box.  
+
||Point to '''co-ordinates''' in '''Values''' box.  
−
| | When angle '''theta''' is 0, '''tan theta''' is ratio of the '''y co-ordinate''' 0 to '''x co-ordinate''' 1 that is 0.  
+
||When angle '''theta''' is 0, '''tan theta''' is ratio of the '''y co-ordinate''' 0 to '''x co-ordinate''' 1 that is 0.  
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | The graph shows angle '''theta''' on the '''x-axis''' and the amplitude of the '''tan theta function''' on the '''y-axis'''.  
+
||The graph shows angle '''theta''' on the '''x-axis''' and the amplitude of the '''tan theta function''' on the '''y-axis'''.  
  
 
At '''angle theta''' 0, as '''tan theta''' is 0, the red point has amplitude of 0.
 
At '''angle theta''' 0, as '''tan theta''' is 0, the red point has amplitude of 0.
 
|-
 
|-
−
| | In the '''Unit Circle''', drag red point CCW to the '''special angle''' 90 '''degrees''' on the '''y-axis'''.  
+
||In the '''Unit Circle''', drag red point CCW to the '''special angle''' 90 '''degrees''' on the '''y-axis'''.  
−
| | In the '''Unit Circle''', drag the red point CCW to the '''special angle''' 90 '''degrees''' on the '''y-axis'''.  
+
|| In the '''Unit Circle''', drag the red point counter clockwise to the '''special angle''' 90 '''degrees''' on the '''y-axis'''.  
 
|-
 
|-
−
| | Point to the '''Values''' box.  
+
||Point to the '''Values''' box.  
−
| | In the '''Values''' box, '''x comma y''' has become '''0 comma 1'''.  
+
||In the '''Values''' box, '''x comma y''' has become '''0 comma 1'''.  
 
|-
 
|-
−
| | Point to the '''Values''' box.  
+
||Point to the '''Values''' box.  
−
| | Note that '''tan theta''' is '''plus or minus infinity''' in the '''Values''' box.
+
||Note that '''tan theta''' is '''plus or minus infinity''' in the '''Values''' box.
 
|-
 
|-
−
| |  
+
||
−
| | Now look at the graph.  
+
||Now look at the graph.  
 
|-
 
|-
−
| | Point to the graph.  
+
||Point to the graph.  
−
| | The red point has moved to 90 '''degrees''' where '''tan theta''' now falls on the vertical dotted line.  
+
||The red point has moved to 90 degrees where '''tan theta''' now falls on the vertical dotted line.  
  
 
This dotted line is the '''vertical asymptote''' of the '''function'''.  
 
This dotted line is the '''vertical asymptote''' of the '''function'''.  
Line 347: Line 336:
 
Here, the '''function''' increases without bound towards '''infinity''' in both directions.  
 
Here, the '''function''' increases without bound towards '''infinity''' in both directions.  
 
|-
 
|-
−
| |  
+
||
−
| | Let us summarize.
+
||Let us summarize.
 
|-
 
|-
−
| | '''Slide Number 10'''
+
||'''Slide Number 10'''
  
 
'''Summary'''
 
'''Summary'''
−
| | In this '''tutorial''', we have demonstrated how to use the '''Trig Tour Phet simulation'''.  
+
||In this tutorial, we have demonstrated how to use the '''Trig Tour Phet simulation'''.  
 
|-
 
|-
−
| | '''Slide Number 11'''
+
||'''Slide Number 11'''
  
 
'''Summary'''
 
'''Summary'''
−
 
  
 
Construct right triangles for a point moving around unit circle
 
Construct right triangles for a point moving around unit circle
  
−
Calculate trigonometric ratios, '''''cos, sin''''' and '''''tan''''', of angle '''ϴ'''
+
Calculate trigonometric ratios, '''cos''', '''sin''' and '''tan''', of angle '''ϴ'''
  
−
Graph '''ϴ''' versus '''''cos, sin''''' and '''''tan''''' '''functions''' along '''x''' and '''y axes'''
+
Graph '''ϴ''' versus '''cos''', '''sin''' and '''tan''' '''functions''' along '''x''' and '''y axes'''
−
| |  
+
||Using this '''simulation''', we have learnt to:
−
 
+
−
Using this '''simulation''', we have learnt to:
+
  
 
Construct right triangles for a point moving around a unit circle
 
Construct right triangles for a point moving around a unit circle
  
−
Calculate trigonometric ratios, '''''cos, sin''''' and '''''tan''''', of angle '''theta'''
+
Calculate trigonometric ratios, '''cos''', '''sin''' and '''tan''', of angle '''theta'''
  
−
Graph '''theta''' versus '''''cos, sin''''' and '''''tan''''' '''functions''' of '''theta''' along '''x''' and '''y axes'''
+
Graph '''theta''' versus '''cos''', '''sin''' and '''tan functions''' of '''theta''' along '''x''' and '''y axes'''.
 
|-
 
|-
−
| | '''Slide Number 12'''
+
||'''Slide Number 12'''
  
 
'''Assignment'''
 
'''Assignment'''
Line 383: Line 369:
 
'''Cosine, sine''' and '''tangent''' values for all '''special angles'''
 
'''Cosine, sine''' and '''tangent''' values for all '''special angles'''
  
−
'''Cos, sin, tangent''' graphs
+
'''Cos''', '''sin''', '''tangent''' graphs
  
 
Relationship between ratios for supplementary angles (sum of 180 '''degrees''')
 
Relationship between ratios for supplementary angles (sum of 180 '''degrees''')
−
| | As an '''assignment''', observe:
+
||As an '''assignment''', observe:
  
 
'''Cosine, sine '''and''' tangent''' values for all '''special angles'''
 
'''Cosine, sine '''and''' tangent''' values for all '''special angles'''
  
−
'''Cosine, sine '''and''' tangent''' graphs
+
'''Cosine, sine''' and '''tangent''' graphs.
  
 
Relationship between ratios for supplementary angles
 
Relationship between ratios for supplementary angles
  
−
The sum of supplementary angles is 180 '''degrees'''.
+
Hint: The sum of supplementary angles is 180 degrees.
 
|-
 
|-
−
| | '''Slide Number 13'''
+
||'''Slide Number 13'''
  
 
'''About the Spoken Tutorial Project'''
 
'''About the Spoken Tutorial Project'''
−
 
  
 
Watch the video available at http://spoken-tutorial.org/ What_is_a_Spoken_Tutorial
 
Watch the video available at http://spoken-tutorial.org/ What_is_a_Spoken_Tutorial
−
 
  
 
It summarizes the Spoken Tutorial project
 
It summarizes the Spoken Tutorial project
−
 
  
 
If you do not have good bandwidth, you can download and watch it
 
If you do not have good bandwidth, you can download and watch it
−
 
+
||The video at the following link summarizes the '''Spoken Tutorial project'''.
−
 
+
−
 
+
−
| | The video at the following link summarizes the '''Spoken Tutorial project'''.
+
  
 
Please download and watch it
 
Please download and watch it
 
|-
 
|-
−
| | '''Slide Number 14'''
+
||'''Slide Number 14'''
  
 
'''Spoken Tutorial workshops'''
 
'''Spoken Tutorial workshops'''
−
| | The '''Spoken Tutorial Project '''team conducts workshops using spoken tutorials and gives certificates on passing online tests.  
+
||The '''Spoken Tutorial Project '''team conducts workshops using spoken tutorials and gives certificates on passing online tests.  
  
 
For more details, please write to us.
 
For more details, please write to us.
 
|-
 
|-
−
| | '''Slide Number 15'''
+
||'''Slide Number 15'''
  
 
'''Forum for specific questions:'''
 
'''Forum for specific questions:'''
Line 435: Line 415:
  
 
Someone from our team will answer them
 
Someone from our team will answer them
−
| | Please post your timed queries in this forum.
+
||Please post your timed queries in this forum.
 
|-
 
|-
−
| | '''Slide Number 16'''
+
||'''Slide Number 16'''
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
| | This project is partially funded by '''Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching'''.
+
||This project is partially funded by '''Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching'''.
 
|-
 
|-
−
| | '''Slide Number 17'''
+
||'''Slide Number 17'''
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
| | '''Spoken Tutorial Project''' is funded by '''NMEICT''', '''MHRD''', Government of India.
+
||'''Spoken Tutorial Project''' is funded by '''NMEICT''', '''MHRD''', Government of India.
  
 
More information on this mission is available at this link.
 
More information on this mission is available at this link.
 
|-
 
|-
−
| |  
+
||
−
| | This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.  
+
||This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.  
  
 
Thank you for joining.  
 
Thank you for joining.  
 
|-
 
|-
 
|}
 
|}

Revision as of 17:14, 11 September 2018

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Trig Tour, an interactive PhET simulation.
Slide Number 2

Learning Objectives

We will demonstrate,

Trig Tour PhET simulation

In this tutorial, we will demonstrate Trig Tour, an interactive PhET simulation.
Slide Number 3

System Requirements

Ubuntu Linux OS version 16.04

Java v 1.8.0

Firefox Web Browser v 60.0.2

Here I am using,

Ubuntu Linux OS version 16.04

Java version 1.8.0

Firefox Web Browser version 60.0.2

Slide Number 4

Pre-requisites

Learners should be familiar with trigonometry.
Slide Number 5

Learning Goals

Construct right triangles for a point moving around a unit circle

Calculate trigonometric ratios, cos, sin and tan, of angle ϴ (theta)

Graph ϴ versus cos, sin and tan functions of ϴ along x and y axes

Using this simulation we will learn how to,

Construct right triangles for a point moving around a unit circle

Calculate trigonometric ratios, cos, sin and tan, of angle theta

Graph theta versus cos, sin and tan functions of theta along x and y axes

Let us begin.
Slide Number 6

Link for PhET simulation


http://phet.colorado.edu

Use the given link to download the simulation.

http://phet.colorado.edu

Point to the file in Downloads folder. I have already downloaded the Trig Tour simulation to my Downloads folder.
Right click on trig-tour_en.html file.

Select Open With Firefox Web Browser option.

Point to the browser address.

To open the simulation, right click on the trig-tour_en.html file.

Select the Open With Firefox Web Browser option.

The file opens in the browser.

Cursor on the interface. This is the interface for the Trig Tour simulation.
Point to each box in the interface.

Point to the reset button.

The interface has four boxes:

Values

Unit circle

Functions, Special angles, labels and grid

Graph

The reset button takes you back to the starting point.

Check Special angles, Labels and Grid in Functions box. In the Functions box, check Special angles, Labels, Grid and click cos.
Slide Number 7

Cosine function

Cosine is ratio of lengths of adjacent side to hypotenuse.

Cosine is x co-ordinate of a point moving around unit circle.

Center of unit circle is origin (0,0).

cos(ϴ) = x/radius = x/1

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

Cosine value is the x co-ordinate of a point moving around a unit circle.

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.

Point to the Unit Circle box. A unit circle is drawn in a Cartesian coordinate system with x and y axes in the Unit Circle box.
Point to the red point.

Point to the blue arrow.

A red point is seen at the circumference of the circle on the x-axis.

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.

Point to the Values box. The Values box contains important values.
Point to the degrees and radians radio buttons. The angle ϴ (theta) can be given in degrees or radians.
Check degrees radio button. Click the degrees radio button.
Point to (x,y) = (1,0) and angle = 0º in the Values box.


Point to the red point in Unit Circle box.

x comma y are co-ordinates 1 comma 0 of the red point at angle theta equals 0 degrees.
Point to cosϴ = x/1 = 1 in Values box. When angle theta equals 0 degrees, x co-ordinate of the red point is 1.
Point to the red point in the Graph box. x-axis of the graph shows angle theta.

y-axis of the graph shows the amplitude of the cos theta function.

At an angle theta of 0 degrees, cos theta is 1.

The red point is at the highest amplitude of 1.

Check degrees radio button. In the Values box, click the radians radio button.
Point to the graph. x axis of the theta vs cos theta graph is converted into radians.

Remember that pi radians are equal to 180 degrees.

One full rotation of 360 degrees is equal to 2 pi radians.

Again, click the degrees radio button.

Point to the empty circles.

In the Functions box, uncheck Special Angles.

You can see empty circles on the unit circle.

In the Functions box, uncheck Special Angles.

Observe how the empty circles disappear.

Check Special Angles. Again, check Special Angles.
Point to the Special Angles. These circles are angles made by the red point with the x-axis as it moves along the circle.

Important angles have been chosen as Special angles.

In the Unit Circle, drag red point counter-clockwise (CCW) to the next special angle.

Point to angle = 30º in Values box and to the red point in the Unit Circle box.

In the Unit Circle, drag the red point counter-clockwise (CCW) to the next special angle.


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

Point to the Values box.

Point to the unit circle.

In the Values box, x comma y is the squareroot of 3 divided by 2 comma half.

In the unit circle, according to Pythagoras’ theorem, x squared plus y squared is 1.

Point to the unit circle. Two square lengths in the Cartesian plane is equal to 1 as radius of unit circle is 1.

y covers only 1 square length and hence, is half.

x covers 1 full and almost three-fourths of a second square.

Point to the Values box. The squareroot of 3 divided by 2 is 0.866.

This is the value of x.

Point to the graph. Look at the graph.

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

Check radians radio button in the Values box.

Point to the Values box and the Graph.

In the Values box, click radians radio button.

This converts 30 degrees into pi divided by 6 radians for theta in the Values box.

Slide Number 8

Sine function

Sine is ratio of lengths of opposite side to hypotenuse.

Sine is y-co-ordinate of a point moving around unit circle.

sin(ϴ) = y/radius = y/1

Sine function

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

Sine value is the y-co-ordinate of the point moving around the same unit circle.


Sine theta is y divided by radius and hence, is y for the unit circle.

Drag the red point back to the x axis. Drag the red point back to the x axis.
In the Functions box, click sin. In the Functions box, click sin.
Check degrees radio button. Click the degrees radio button.
Point to the Values box.

Point to the unit circle.

As seen earlier, x comma y are 1 comma 0.

Note the definitions of sine theta given earlier.

When angle theta is 0 degrees, the y co-ordinate of the red point is 0.

Point to the graph. The graph shows angle theta on the x-axis and the amplitude of the sine theta function on the y-axis.
Point to the graph. At angle theta of 0 degrees, as sine theta is 0, the red point has amplitude 0.
In the Unit Circle, drag red point CCW to the next special angle 30 degrees. In the Unit Circle, drag the red point counter clockwise to the next special angle 30 degrees.
Point to the Values box. In the Values box, note that x comma y is squareroot of 3 divided by 2 comma half.

Remember how you can calculate these.

Point to the graph. In the graph, the red point has moved to 30 degrees along the sine function.

Its amplitude is 0.5 or half.

Slide Number 9

Tangent function

Tangent is ratio of lengths of opposite to adjacent sides.

tan(ϴ) = sinϴ/cosϴ = y/x

Tangent function

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


Tan theta is the ratio of sin theta to cos theta and to y divided by x.

Drag the red point back to the x-axis, that is to (1,0). Drag the red point back to the x-axis that is to 1 comma 0.
Click tan in Functions box. In the Functions box, click tan.
Point to co-ordinates in Values box. When angle theta is 0, tan theta is ratio of the y co-ordinate 0 to x co-ordinate 1 that is 0.
Point to the graph. The graph shows angle theta on the x-axis and the amplitude of the tan theta function on the y-axis.

At angle theta 0, as tan theta is 0, the red point has amplitude of 0.

In the Unit Circle, drag red point CCW to the special angle 90 degrees on the y-axis. In the Unit Circle, drag the red point counter clockwise to the special angle 90 degrees on the y-axis.
Point to the Values box. In the Values box, x comma y has become 0 comma 1.
Point to the Values box. Note that tan theta is plus or minus infinity in the Values box.
Now look at the graph.
Point to the graph. The red point has moved to 90 degrees where tan theta now falls on the vertical dotted line.

This dotted line is the vertical asymptote of the function.

It represents the value of x which the function approaches but never touches.

Here, the function increases without bound towards infinity in both directions.

Let us summarize.
Slide Number 10

Summary

In this tutorial, we have demonstrated how to use the Trig Tour Phet simulation.
Slide Number 11

Summary

Construct right triangles for a point moving around unit circle

Calculate trigonometric ratios, cos, sin and tan, of angle ϴ

Graph ϴ versus cos, sin and tan functions along x and y axes

Using this simulation, we have learnt to:

Construct right triangles for a point moving around a unit circle

Calculate trigonometric ratios, cos, sin and tan, of angle theta

Graph theta versus cos, sin and tan functions of theta along x and y axes.

Slide Number 12

Assignment

Observe:

Cosine, sine and tangent values for all special angles

Cos, sin, tangent graphs

Relationship between ratios for supplementary angles (sum of 180 degrees)

As an assignment, observe:

Cosine, sine and tangent values for all special angles

Cosine, sine and tangent graphs.

Relationship between ratios for supplementary angles

Hint: The sum of supplementary angles is 180 degrees.

Slide Number 13

About the Spoken Tutorial Project

Watch the video available at http://spoken-tutorial.org/ What_is_a_Spoken_Tutorial

It summarizes the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it

Slide Number 14

Spoken Tutorial workshops

The Spoken Tutorial Project team conducts workshops using spoken tutorials and gives certificates on passing online tests.

For more details, please write to us.

Slide Number 15

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them

Please post your timed queries in this forum.
Slide Number 16

Acknowledgement

This project is partially funded by Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching.
Slide Number 17

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Vidhya Iyer from IIT Bombay, signing off.

Thank you for joining.

Contributors and Content Editors

Madhurig, Snehalathak, Vidhya

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