Madhurig at 06:49, 26 May 2021

2021-05-26T06:49:18Z

Madhurig: Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- ||'''Slide Number 1''' '''Title Slide''' ||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'..."

2021-05-06T09:01:30Z

Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- ||'''Slide Number 1''' '''Title Slide''' ||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'..."

New page

{|border=1
||'''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/ http://phet.colorado.edu]
||Use the given link to download the '''simulation'''.

[http://phet.colorado.edu/ 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 function'''

'''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.
|-
|}

@@ Line 55: / Line 55: @@
 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'''.
 |-
 ||
@@ Line 109: / Line 109: @@
 '''Cosine function'''
-'''Cosine''' is ratio of lengths of adjacent side to hypotenuse.
+'''Cosine''' is the ratio of lengths of adjacent side to hypotenuse.
 '''Cosine''' is '''x co-ordinate''' of a point moving around unit circle.
@@ Line 169: / Line 169: @@
 |-
 ||Point to the graph.
-||x axis of the '''theta''' vs '''cos theta''' graph is converted into '''radians'''.
+||x axis of the '''theta''' versus '''cos theta''' graph is converted into '''radians'''.
 Remember that '''pi radians''' are equal to '''180 degrees'''.
@@ Line 252: / Line 252: @@
 '''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'''.

PhET-Simulations-for-Mathematics/C2/Trig-Tour/English - Revision history

Madhurig at 06:49, 26 May 2021

Madhurig: Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- ||'''Slide Number 1''' '''Title Slide''' ||Welcome to this tutorial on '''Trig Tour''', an '''interactive PhET simulation'..."