Applications-of-GeoGebra/C2/Trigonometric-Ratios-and-Graphs/English-timed
From Script | Spoken-Tutorial
Time | Narration |
00:01 | Welcome to this tutorial on Trigonometric Ratios and Graphs. |
00:06 | In this tutorial, we will learn how to use GeoGebra to, |
00:11 | Calculate trigonometric ratios |
00:15 | Plot corresponding graphs |
00:18 | To follow this tutorial, you should be familiar with GeoGebra interface |
00:25 | Previous tutorials in this series |
00:28 | If not, for relevant tutorials, please visit our website |
00:34 | Here, I am using
Ubuntu Linux OS version 14.04 |
00:42 | GeoGebra 5.0.388.0 hyphen d |
00:48 | I have opened GeoGebra interface with a unit circle and a right triangle A C Bprime. |
00:59 | Sine function |
01:01 | Sine of an angle is the ratio of the lengths of the opposite side to the hypotenuse. |
01:08 | Angle B prime A C is equal to alpha degrees and to beta degrees |
01:15 | In triangle A Bprime C, sine alpha equals ratio of the lengths B prime C to A B prime. |
01:23 | This is also equal to ratio of y co-ordinate of B prime to radius. |
01:30 | Here, sine alpha is y co-ordinate of point B prime. |
01:36 | Click on Options menu. |
01:39 | Select Rounding and then 3 Decimal Places. |
01:44 | All the ratios will now have 3 decimal places. |
01:49 | Now let us show sine alpha values using the input bar. |
01:55 | In input bar, type SINE is equal to y B prime in parentheses divided by radius.
Press Enter. |
02:08 | Sine values are displayed in Algebra view. |
02:12 | Drag alpha slider to 0 and then to 360 degrees. |
02:20 | Observe the change in sine values in Algebra view. |
02:25 | Observe that sine value remains positive as long as y axis values are positive. |
02:32 | Click on Point tool. |
02:35 | Click on the screen outside the circle in Graphics view. |
02:40 | Point D appears outside the circle. |
02:44 | Set alpha to 0 degrees on the slider. |
02:48 | Right-click on D and click on Object Properties. |
02:53 | Select Color tab and choose red. |
02:57 | Close the Preferences window. |
03:00 | Again, right-click on D and check Trace On option. |
03:06 | In Algebra view, double click on D. |
03:10 | Delete co-ordinates of D. |
03:14 | Select symbol alpha, click on the letter alpha. |
03:19 | Insert alpha as x co-ordinate of D. |
03:23 | Type SINE as y co-ordinate of D, and press Enter. |
03:29 | D has been changed to alpha comma SINE. |
03:34 | GeoGebra will convert alpha into radians. |
03:39 | The alpha value in radians is the x co-ordinate of D. |
03:43 | Its y co-ordinate is the SINE value of alpha. |
03:47 | This will make D trace the sine function as you change angle alpha. |
03:53 | We want to see 2 pi radians along the positive side of the x axis. |
03:59 | Under Move Graphics View, click once on Zoom Out and then twice in Graphics view. |
04:09 | Click on Move Graphics View tool. |
04:13 | Click on Graphics background and when hand symbol appears, move Graphics view. |
04:20 | You should see the circle and 2 pi radians along positive side of x axis. |
04:29 | Increase alpha on the slider from 0 to 360 degrees 2 pi radians. |
04:38 | Point D will trace the sine function graph. |
04:42 | Sine values remain positive as long as y values are positive. |
04:49 | In input bar, type d x in parentheses is equal to sin x in parentheses and press Enter. |
05:00 | Sine function will be graphed beyond minus 2 pi and plus 2 pi radians. |
05:07 | Click on and move Graphics view to see d of x beyond minus 2 pi and plus 2 pi radians. |
05:17 | Note that this will erase traces of D. |
05:22 | Click on and move Graphics view to see circle and plus 2 pi radians along x axis. |
05:30 | Again drag slider alpha to 0 degrees to see traces of D. |
05:37 | Compare d of x with traces of D. |
05:42 | Cosine function |
05:44 | Cosine of an angle is the ratio of the lengths of the adjacent side to the hypotenuse. |
05:51 | Cos alpha is equal to the following ratios. |
05:55 | Length of AC to length of AB prime and x co-ordinate of B prime to radius. |
06:03 | In this unit circle, cos alpha corresponds to x co-ordinate of point B prime. |
06:10 | Right-click on point D and uncheck Trace On option. |
06:16 | Click on and move Graphics view slightly to erase traces of D. |
06:22 | In input bar, type the following line. |
06:26 | COSINE is equal to x B prime in parentheses divided by radius.
Press Enter. |
06:38 | Cosine value is displayed in Algebra view. |
06:42 | Drag slider alpha from 0 to 360 degrees. |
06:48 | Observe how cosine values change in Algebra view. |
06:52 | Note how cosine remains positive as long as x axis values are positive. |
06:59 | Click on Point tool and click outside the circle. |
07:05 | Point E appears outside the circle. |
07:08 | Drag slider alpha to 0 degrees. |
07:12 | Right-click on E, click on Object Properties. |
07:17 | Select Color tab and choose brown. |
07:22 | Close the Preferences window. |
07:25 | Right-click on E, check Trace On option. |
07:30 | In Algebra view, double click on E. |
07:34 | Delete co-ordinates of E. |
07:37 | Select symbol alpha, click on the letter alpha. |
07:43 | Insert alpha as x co-ordinate of E. |
07:47 | Type COSINE instead of y co-ordinate of E, and press Enter. |
07:55 | E has been changed to alpha comma COSINE. |
08:00 | Drag slider alpha from 0 to 360 degrees. |
08:06 | Point E will trace the cosine function graph. |
08:11 | In input bar, type e x in parentheses is equal to cos x in parentheses.
Press Enter. |
02:33 | Cosine function e of x will be graphed beyond minus 2 pi and plus 2 pi radians. |
08:33 | Click and move Graphics view to see e of x beyond minus 2 pi and plus 2 pi radians. |
08:44 | This will erase traces of E. |
08:48 | Click on and move Graphics view to see plus 2 pi radians along x axis. |
08:57 | Again drag slider alpha to 0 degrees to see traces of E. |
09:04 | Compare the graph of e of x with traces of E. |
09:09 | Right-click on E and uncheck Trace On option. |
09:15 | Click on and move Graphics view slightly to erase traces of E. |
09:21 | Tangent function
Tangent of an angle is the ratio of lengths of the opposite side to the adjacent side. |
09:30 | Tan alpha is the ratio of sine alpha to cos alpha and the ratio of lengths of B prime C to AC. |
09:39 | Tan alpha is also the ratio of the y co-ordinate to x co-ordinate of B prime. |
09:45 | In input bar, type the following line. |
09:50 | TANGENT is equal to y B prime in parentheses divided by x B prime in parentheses.
Press Enter. |
10:01 | Tangent value is displayed in Algebra view. |
10:05 | Drag alpha slider from 0 to 360 degrees. |
10:11 | Observe how tangent values change in Algebra view. |
10:15 | Click on Point tool and click outside the circle. |
10:21 | Point F appears outside the circle. |
10:24 | Set alpha to 0 degrees on the slider. |
10:28 | Right-click on F and select Object Properties. |
10:33 | Select Color tab and choose green. |
10:39 | Close the Preferences window. |
10:42 | Again right-click on F, check Trace On option. |
10:48 | In Algebra view, scroll down and double click on F. |
10:54 | Delete co-ordinates of F. |
10:58 | Select symbol alpha, click on the letter alpha. |
11:03 | Insert alpha as x co-ordinate of F. |
11:07 | Type TANGENT as y co-ordinate of F, and press Enter. |
11:13 | F has been changed to alpha comma TANGENT. |
11:18 | Point F will trace the tangent function graph as alpha value changes. |
11:24 | Increase alpha on the slider from 0 to 360 degrees 2 pi radians. |
11:32 | F increases from origin to infinity. |
11:37 | Note vertical asymptote at pi divided by 2 radians. |
11:42 | Tangent value is plus infinity at pi divided by 2 radians. |
11:49 | It is minus infinity at 3 pi divided by 2 radians. |
11:55 | In input bar, type f x in parentheses is equal to tan x in parentheses and press Enter. |
12:07 | The tangent function is graphed beyond minus 2 pi and plus 2 pi radians. |
12:16 | Click on and move Graphics view to see graph of f of x beyond minus 2 pi and plus 2 pi radians. |
12:28 | Click on and move Graphics view to see plus 2 pi radians along x axis. |
12:37 | Drag slider alpha back to 0 degrees to see traces of F. |
12:43 | Also compare the tangent function f of x with traces of F. |
12:50 | Let us summarize. |
12:52 | In this tutorial, we have learnt
how to use GeoGebra to calculate and graph sin alpha, cos alpha and tan alpha |
13:03 | Assignment
Try these steps to graph secant, cosecant and cotangent functions. |
13:12 | Analyze the link between sine values for supplementary angles
angles whose sum is 180 degrees. |
13:21 | Analyze the link between sine and cosine values for supplementary angles. |
13:27 | The video at the following link summarizes the Spoken Tutorial Project.
Please download and watch it. |
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14:01 | This is Vidhya Iyer from IIT Bombay signing off.
Thank you for joining. |