PhET-Simulations-for-Mathematics/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.
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11:55	This is Vidhya Iyer from IIT Bombay, signing off. Thank you for joining.

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