Difference between revisions of "PhET-Simulations-for-Mathematics/C2/Trig-Tour/English"
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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'''. |
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'''Cosine function''' | '''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. | '''Cosine''' is '''x co-ordinate''' of a point moving around unit circle. | ||
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||Point to the graph. | ||Point to the graph. | ||
| − | ||x axis of the '''theta''' | + | ||x axis of the '''theta''' versus '''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'''. | ||
| Line 252: | Line 252: | ||
'''Sine 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'''. | ||
Latest revision as of 12:19, 26 May 2021
| 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 |
Use the given link to download the simulation. |
| 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 the 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.
|
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 versus 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.
|
| 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.
|
| 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.
|
| 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. |
