Applications-of-GeoGebra/C2/Inverse-Trigonometric-Functions/English

Visual Cue	Narration
Slide Number 1 Title Slide	Welcome to this tutorial on Inverse Trigonometric Functions.
Slide Number 2 Learning Objectives	In this tutorial, we will learn to use GeoGebra to Plot graphs of inverse trigonometric functions Compare them to graphs of trigonometric functions Create check-boxes to group and show or hide functions
Slide Number 3 Pre-requisites www.spoken-tutorial.org	To follow this tutorial, you should be familiar with: GeoGebra interface Trigonometry For relevant tutorials, please visit our website.
Slide Number 4 System Requirement	Here I am using: Ubuntu Linux OS version 14.04 GeoGebra 5.0.388.0-d
Show the GeoGebra window.	I have already opened the GeoGebra interface.
Switching x axis to radians Double click on x axis in Graphics view >> Object Properties	Now let us change x Axis units to radians. In Graphics view, double-click on the x axis and then on Object Properties.
Click on Preferences-Graphics >> x Axis.	In the Object Properties menu, click on Preferences-Graphics and then on xAxis.
Check the Distance option, select π/2 >> select Ticks first option	Check the Distance option, select pi divided by 2 and then the Ticks first option.
Close the Preferences box.	Close the Preferences box.
Point to x-axis.	Units of x-axis are in radians with interval of pi divided by 2 as shown. GeoGebra will convert degrees of angle alpha to radians.
Point to the toolbar.	Note that the name appears when you place the mouse over any tool icon in the toolbar.
Click on Slider tool >> click on Graphics view.	In the Graphics toolbar, click on Slider and then in the top of Graphics view.
Point to the Slider dialog box.	A slider dialog-box appears.
Point to Number radio button.	By default, Number radio-button is selected.
Type Name as symbol theta ϴ.	In the Name field, select theta from the Symbol menu.
Point to Min, Max and Increment values. Click OK.	Type the Min value as minus 360 and Max plus 360 with Increment 1. Click OK.
Point to slider ϴ.	This creates a number slider theta from minus 360 to plus 360.
In input bar, type α = (ϴ /180) π. Point to space between the right parenthesis and pi for multiplication. Press Enter	In the input bar, type alpha is equal to theta divided by 180 in parentheses, and then pi. Note how GeoGebra inserts a space between the right parenthesis and pi for multiplication. Press Enter.
Drag slider ϴ to -360 and then back to 360.	Drag slider theta to minus 360 and then back to 360.
Point to values of α in Algebra view.	In Algebra view, observe how alpha changes from minus 2pi to 2pi radians as you change theta.
Drag slider ϴ to minus 360.	Drag slider theta back to minus 360.
Sine function In input bar, type f_S: = Function[sin(x), -2π, α] >> press Enter.	In the input bar, type the following command: f underscore S colon is equal to Function with capital F Type the following words in square brackets. sin, x in parentheses, comma minus 2 pi comma alpha. Press Enter.
Drag boundary to see Algebra view properly.	Drag the boundary to see Algebra view properly.
Point to fS in Algebra view.	Here, fS defines the sine function of x. x is between -2 pi and alpha which can take a maximum value of 2pi. This is called the domain of the function.
Drag the boundary to see Graphics View properly.	Drag the boundary to see Graphics View properly.
Drag slider theta from minus 360 to 360.	Drag slider theta from minus 360 to 360.
Point to fS sine function graph.	This graphs the sine function of x.
In the toolbar, click on the bottom right triangle of the last button. Point to Move Graphics View button.	In the toolbar, click on the bottom right triangle of the last button. Note that this button is called Move Graphics View.
Under Move Graphics View, click on Zoom Out tool. Click on Graphics view to see 2 pi radians on either side of origin.	In the menu that appears, click on Zoom Out. Click in Graphics view to see 2 pi radians on either side of the origin.
Again, click on Move Graphics View and drag the background to see the graph properly.	Again, click on Move Graphics View and drag the background to see the graph properly.
Drag slider ϴ back to -360.	Drag slider theta back to minus 360.
Slide Number 5 Inverse Trigonometric Functions e.g., If sin-1z (or arcsin z) = w, then z = sin w Restrict domain of trigonometric function, define principal value Interchange x and y axes Change curvature of trigonometric function graph	Inverse Trigonometric Functions For example, If inverse sine of z (also known as arcsin of z) is w. Then, z is sin w. w can have multiple values. So a principal value has to be defined and the domain has to be restricted. To get the inverse function graph, interchange x and y axes. Next, change curvature of trigonometric function graph. You can pause and refer to the example in the additional material provided for this tutorial.
	Let us go back to the GeoGebra window.
Inverse sine function Type i_S: = Function[asin(x), -1, 1] in input bar >> press Enter.	In the input bar, type the following command: i underscore S colon is equal to Function with capital F Type the following words in square brackets. asin, x in parentheses, comma minus 1 comma 1 Press Enter.
Drag the boundary to see Algebra view properly.	Drag the boundary to see Algebra view properly.
Point to iS function graph.	This graphs the inverse sine (or arc sine) function of x. Note that x and y axes are interchanged for this inverse sine function. Its domain (set of x values) lies between minus 1 and 1. Observe the graph.
Drag the boundary to see Graphics view properly.	Drag the boundary to see Graphics view properly.
Type P_S = (sin(α), α) in input bar >> press Enter	In the input bar, type the following command: P underscore S colon is equal to Type the following words in parentheses. sin alpha in parentheses comma alpha Press Enter.
Point to PS.	This creates point PS on the inverse sine graph. On the sine function graph, PS would be alpha comma sine alpha.
In Algebra view, right-click on PS, check Trace On option.	In Algebra view, right-click on PS, check the Trace On option.
Drag slider ϴ to 360.	Drag slider theta to 360.
Point to traces of PS, iS and FS.	Traces appear for the inverse sine function graph for alpha. fs also appears in Graphics view. Compare iS and traces of PS. Note that the domain for the graph that PS traces is not restricted from -1 to 1.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Click and drag the background in Graphics view to erase traces of PS.	Click and drag the background in Graphics view to erase traces of PS.
In Algebra view, uncheck fS, iS and PS.	In Algebra view, uncheck fS, iS, and PS to hide them.
Slide Number 6 Cosine and Inverse Cosine Functions Cosine function fC in domain [-2π, α] Inverse cosine function iC in domain [-1,1] PC (cos(α),α)	Cosine and Inverse Cosine Functions Follow the steps shown for SINE to graph the cosine function fC. Its domain should be from -2 pi to alpha. Graph the inverse cosine function iC" in the domain from -1 to 1. Create a point PC whose co-ordinates are cos alpha comma alpha. The domain of the inverse cosine graph that PC traces will go beyond -1 and 1.
Point to fC, iC and traces of PC in Graphics view.	The cosine and inverse cosine functions should look like this.
In Algebra view, uncheck fC, iC and PC and move the background to erase traces of PC.	In Algebra view, uncheck fC, iC and PC and move the background to erase traces of PC.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Slide Number 7 Tangent and Inverse Tangent Functions Tangent function fT in domain [-2π, α] Inverse tangent function iT in domain [-∞, ∞] PT (tan(α),α)	Tangent and Inverse Tangent Functions Now graph the tangent function fT. Its domain should also be from -2 pi to alpha. We will look at the graph for the inverse tangent function iT. Its domain will be from minus infinity to infinity. Create a point PT whose co-ordinates are tan alpha comma alpha. The domain of the inverse tangent graph that PT traces will go beyond -1 and 1.
	Let us look at the inverse tangent function graph in the domain from -1 to 1.
Inverse tangent function Type i_T: = Function[atan(x), -∞, ∞] in input bar >> press Enter.	To type infinity, click in the input bar and on symbol alpha appearing at the right end of the bar. In the symbol menu, click on the infinity symbol in the third row and third column from the right. In the input bar, type the following command: i underscore T colon is equal to Function with capital F Type the following words in square brackets. atan, x in parentheses, comma minus infinity comma infinity Press Enter.
Point to iT function graph.	This graphs the inverse tangent function of x. x lies between minus infinity and infinity. Observe the graph.
Drag slider ϴ to 360.	Drag slider theta to 360.
Point to traces of PT and iT.	Compare traces of PT and iT.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Drag the background.	Drag the background slightly to the erase the traces of PT
In Algebra view, uncheck fT and PT.	In Algebra view, uncheck fT and PT.
In Algebra view, check fS, iS, iC, PS and PC to show them again.	In Algebra view, check fS, iS, and PS to show them again.
cursor on the window.	Let us create check boxes to make it easier to group and see different functions at a time.
Check boxes Under Slider, click on check box tool. Click on the top of the grid in Graphics view.	Under Slider, click on Check-box. Click on the top of the grid in Graphics view.
Point to the dialog box.	ACheck-Box to Show/Hide Objects dialog-box appears.
Type SIN as caption.	In the Caption field, type SIN.
Click on Objects >> select fS, iS and PS >> apply	Click on Objects drop-down menu to select fS, iS and PS, one by one, click Apply.
Point to check box SIN.	A check-box SIN is created in Graphics view. It gives us the option to display or hide sine, arcsine graphs and point PS.
Click on Check Box. Click on the top of the grid in Graphics view.	Again, click on Check Box. Click on the top of the grid in Graphics view.
Point to the dialog box.	A Check-Box to Show/Hide Objects dialog-box appears.
Type TAN as caption.	In the Caption field, type TAN.
Click on Objects >> select fT, iT and PT >> apply.	Click on Objects drop-down menu to select fT, iT and PT, one by one, click Apply.
Point to check box TAN.	A check-box TAN is created in Graphics view. It gives us the option to display or hide tangent, arctangent graphs and point PT.
Click on Move tool to uncheck all boxes.	In the toolbar, click on the first Move button and un-check all boxes.
Check SIN box.	Check the SIN box.
Drag slider theta to 360.	Drag slider theta to 360.
Point to fS, iS and traces of PS in Graphics view.	Observe fS, iS and traces of PS appear in Graphics view.
Uncheck SIN box.	Uncheck the SIN box.
Click on and move Graphics view slightly to erase traces of PS.	Click on and move Graphics view slightly to erase traces of PS.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Check TAN box.	Check the TAN box.
Drag slider theta to 360.	Drag slider theta to 360.
Point to fT, iT and traces of PT in Graphics view.	Observe fT, iT and traces of PT appear in Graphics view.
Drag slider theta back to minus 360.	Drag slider theta back to minus 360.
Check the SIN box.	Check the SIN box.
Drag slider theta to 360.	Drag slider theta to 360.
Point to all the functions in Graphics view.	Observe the functions appearing in Graphics view.
	Let us summarize.
Slide Number 8 Summary	In this tutorial, we have learnt how to use GeoGebra to: Graph trigonometric functions Graph inverse trigonometric functions Create check-boxes to group and show/hide functions
Slide Number 9 Assignment	As an assignment, Plot graphs of, Secant and arcsecant Cosecant and arccosecant Cotangent and arccotangent For hints, you can refer to the additional material provided.
Slide Number 10 About Spoken Tutorial project	The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
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Slide Number 12 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 on this forum.
Slide Number 13 Acknowledgement	The 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.

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