PhET/C2/Trig-tour/English-timed
Time | Narration |
00:01 | Welcome to this tutorial on Trig Tour, an interactive PhET simulation. |
00:07 | In this tutorial, we will demonstrate Trig Tour, an interactive PhET simulation. |
00:15 | Here I am using, Ubuntu Linux OS version 16.04 |
00:22 | Java version 1.8.0 |
00:26 | Firefox Web Browser version 60.0.2 |
00:32 | Learners should be familiar with trigonometry. |
00:36 | Using this simulation we will learn how to,
Construct right triangles for a point moving around a unit circle |
00:47 | Calculate trigonometric ratios, cos, sin and tan, of angle theta |
00:54 | Graph theta versus cos, sin and tan functions of theta along x and y axes |
01:01 | Let us begin. |
01:03 | Use the given link to download the simulation. |
01:08 | I have already downloaded the Trig Tour simulation to my Downloads folder. |
01:14 | To open the simulation, right click on the trig-tour html file. |
01:20 | Select the Open With Firefox Web Browser option.
The file opens in the browser. |
01:29 | This is the interface for the Trig Tour simulation. |
01:34 | The interface has four boxes:
Values Unit circle |
01:41 | Functions, Special angles, labels and grid
Graph |
01:48 | The reset button takes you back to the starting point. |
01:53 | In the Functions box, check Special angles, Labels, Grid and click cos. |
02:05 | Cosine function
Cosine of an angle is the ratio of the lengths of the adjacent side to the hypotenuse. |
02:15 | Cosine value is the x co-ordinate of a point moving around a unit circle. |
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. |
02:38 | A unit circle is drawn in a Cartesian coordinate system with x and y axes in the Unit Circle box. |
02:49 | A red point is seen at the circumference of the circle on the x-axis. |
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. |
03:07 | The Values box contains important values. |
03:12 | The angle ϴ (theta) can be given in degrees or radians. |
03:17 | Click the degrees radio button. |
03:20 | x comma y are co-ordinates 1 comma 0 of the red point at angle theta equals 0 degrees. |
03:30 | When angle theta equals 0 degrees, x co-ordinate of the red point is 1. |
03:38 | x-axis of the graph shows angle theta. |
03:43 | y-axis of the graph shows the amplitude of the cos theta function. |
03:49 | At an angle theta of 0 degrees, cos theta is 1. |
03:54 | The red point is at the highest amplitude of 1. |
03:59 | In the Values box, click the radians radio button. |
04:04 | x axis of the theta vs cos theta graph is converted into radians. |
04:11 | Remember that pi radians are equal to 180 degrees. |
04:17 | One full rotation of 360 degrees is equal to 2 pi radians.
Again, click the degrees radio button. |
04:29 | You can see empty circles on the unit circle.
In the Functions box, uncheck Special Angles. |
04:39 | Observe how the empty circles disappear. |
04:43 | Again, check Special Angles. |
04:47 | These circles are angles made by the red point with the x-axis as it moves along the circle. |
04:56 | Important angles have been chosen as Special angles. |
05:01 | In the Unit Circle, drag the red point counter-clockwise (CCW) to the next special angle. |
05:09 | The red point has moved 30 degrees in the counter-clockwise direction along the circle. |
05:16 | In the Values box, x comma y is the squareroot of 3 divided by 2 comma half. |
05:25 | In the unit circle, according to Pythagoras’ theorem, x squared plus y squared is 1. |
05:34 | Two square lengths in the Cartesian plane is equal to 1 as radius of unit circle is 1. |
05:44 | y covers only 1 square length and hence, is half. |
05:50 | x covers 1 full and almost three-fourths of a second square. |
05:57 | The squareroot of 3 divided by 2 is 0.866.
This is the value of x. |
06:07 | Look at the graph.
The red point has moved to 30 degrees along the cos function. |
06:15 | In the Values box, click radians radio button. |
06:20 | This converts 30 degrees into pi divided by 6 radians for theta in the Values box. |
06:29 | Sine function
Sine of an angle is the ratio of the lengths of the opposite side to the hypotenuse. |
06:39 | Sine value is the y-co-ordinate of the point moving around the same unit circle. |
06:47 | Sine theta is y divided by radius and hence, is y for the unit circle. |
06:56 | Drag the red point back to the x axis. |
07:00 | In the Functions box, click sin. |
07:04 | Click the degrees radio button. |
07:07 | As seen earlier, x comma y are 1 comma 0. |
07:13 | Note the definitions of sine theta given earlier. |
07:18 | When angle theta is 0 degrees, the y co-ordinate of the red point is 0. |
07:25 | The graph shows angle theta on the x-axis and the amplitude of the sine theta function on the y-axis. |
07:34 | At angle theta of 0 degrees, as sine theta is 0, the red point has amplitude 0. |
07:43 | In the Unit Circle, drag the red point counter clockwise to the next special angle 30 degrees. |
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. |
08:04 | In the graph, the red point has moved to 30 degrees along the sine function.
Its amplitude is 0.5 or half. |
08:17 | Tangent function
Tangent of an angle is the ratio of the lengths of opposite side to adjacent side. |
08:27 | Tan theta is the ratio of sin theta to cos theta and to y divided by x. |
08:35 | Drag the red point back to the x-axis that is to 1 comma 0. |
08:44 | In the Functions box, click tan. |
08:48 | When angle theta 0, tan theta is ratio of the y co-ordinate 0 to x co-ordinate 1 that is 0. |
09:00 | The graph shows angle theta on the x-axis and the amplitude of the tan theta function on the y-axis. |
09:09 | At angle theta 0, as tan theta is 0, the red point has amplitude of 0. |
09:17 | In the Unit Circle, drag the red point counter clockwise to the special angle 90 degrees on the y-axis. |
09:27 | In the Values box, x comma y has become 0 comma 1. |
09:33 | Note that tan theta is plus or minus infinity in the Values box. |
09:40 | Now look at the graph. |
09:43 | The red point has moved to 90 degrees where tan theta now falls on the vertical dotted line. |
09:53 | This dotted line is the vertical asymptote of the function. |
09:58 | It represents the value of x which the function approaches but never touches. |
10:05 | Here, the function increases without bound towards infinity in both directions. |
10:13 | Let us summarize. |
10:16 | In this tutorial, we have demonstrated how to use the Trig Tour Phet simulation. |
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. |
10:46 | As an assignment, observe: Cosine, sine and tangent values for all special angles |
10:53 | Cosine, sin and tangent graphs. |
10:57 | Relationship between ratios for supplementary angles
The sum of supplementary angles is 180 degrees. |
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. |
11:33 | This project is partially funded by Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching. |
11:42 | Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
More information on this mission is available at this link. |
11:55 | This is Vidhya Iyer from IIT Bombay, signing off.
Thank you for joining. |