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 plot graphs of inverse trigonometric functions in GeoGebra.
Slide Number 3 Pre-requisites www.spoken-tutorial.org	To follow this tutorial, you should be familiar with: GeoGebra interface Trigonometry and related graphs If not, 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
Slide Number 5 Inverse trigonometric functions	Arcsine, arccosine, arctangent etc are inverse trigonometric functions. These ratios of right triangle lengths help to calculate the angle
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. Double-click on x axis in Graphics view and then on Object Properties.
Click on Preferences-Graphics >> x axis.	In Object Properties menu, click on Preferences-Graphics and then on x Axis.
Check the Distance option, select π/2 >> select Ticks first option	Check the Distance option, select pi divided by 2 and then 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.
Click on Slider tool >> click on Graphics view.	Click on Slider tool and then click on Graphics view.
Point to the Slider dialog box.	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 Symbol menu.
Point to Min, Max and Increment values. Click OK button.	Type the Min value as minus 360 and Max plus 360 with Increment 1. Click OK button.
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 input bar, type alpha is equal to theta divided by 180 in parentheses pi. Note how GeoGebra inserts a space between the right parenthesis and pi for multiplication. Press Enter.
Drag slider ϴ to -360 and then to 360.	Drag slider theta from minus 360 to plus 360.
Point to values of α in Algebra view.	In Algebra view, observe how alpha changes from minus 2 pi to plus 2 pi radians.
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 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. Here, defines the sine function of x.
Under Move Graphics View, click on Zoom Out tool. Click on Graphics view to see 2 pi radians on either side of origin.	Under Move Graphics View, click on Zoom Out tool. Click on Graphics view to see 2 pi radians on either side of the origin.
Drag slider ϴ to 360.	Drag slider theta from minus 360 to plus 360.
Point to fS sine function graph.	This graphs sine function of x. Domain of x is between minus 2 pi and alpha. That is,x lies between minus 2 pi and alpha. Observe the graph of fS.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Inverse sine function Type i_S: = Function[asin(x), -1, 1] in input bar >> press Enter.	In input bar, type the following command: i underscore S colon is equal to Function with capital F Type the following words in square brackets. a sin x in parentheses comma minus 1 comma 1” Press Enter.
Point to iS function graph.	This graphs inverse sine (or arc sine) function of x. x lies between minus 1 and plus 1. Observe the graph.
Type P_S = (sin(α), α) in input bar >> press Enter	In 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.
In Algebra view, right-click on PS, check Trace On option.	In Algebra view, right-click on PS, check Trace On option.
Drag slider ϴ to 360.	Drag slider theta to 360.
Point to traces of PS, iS and FS.	Traces appear for inverse sine function graph for alpha. fs also appears in Graphics view. Compare iS and traces of PS.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Click on and move Graphics view to erase traces of PS.	Click on and move 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.
Cosine function Type f_C: = Function[cos(x), -2π, α] in input bar >> press Enter.	In input bar, type the following command: f underscore C colon is equal to Function with capital F Type the following words in square brackets. cos x in parentheses comma minus 2 pi comma alpha. Press Enter. Here, fC defines the cosine function.
Drag slider ϴ to 360.	Drag slider theta to 360.
Point to fC function graph.	This graphs the cos x function. x lies between minus 2 pi and alpha. Observe the graph.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Inverse cosine function Type i_C: = Function[acos(x), -1, 1] in input bar >> press Enter.	In input bar, type the following command: i underscore C colon is equal to Function with capital F Type the following words in square brackets. acos x in parentheses comma minus 1 comma 1. Press Enter. Here, IC defines the inverse cosine (or arccosine) function of x.
Point to iC function graph.	This graphs the inverse cosine (or arccosine) function of x. The domain of x is from minus 1 to plus 1. Observe the graph.
Point on cosine function. Type P_C = (cos(α), α) in input bar >> press Enter	In input bar, type the following command: P underscore C colon is equal to Type the following words in parentheses. cos alpha in parentheses comma alpha Press Enter.
Point to Pc.	This creates a point PC.
In Algebra view, right-click on PC check Trace On option.	In Algebra view, right-click on PC, check Trace On option.
Drag slider ϴ from 0 to 360.	Drag slider theta to 360.
Point to traces of PC, iC and FC.	Traces appear for inverse cosine function graph for alpha. FC also appears in Graphics view. Compare iC and traces of PC.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Click on and move Graphics view to erase traces of PC.	Click on and move Graphics view to erase traces of PC.
In Algebra view, uncheck fC, iC and PC to hide them.	In Algebra view, uncheck fC, iC and PC to hide them.
Tangent function Type f_T: = Function[tan(x), -2π, α] in input bar >> press Enter.	In input bar, type the following command: f underscore T colon is equal to Function with capital F Type the following words in square brackets. Tan x in parentheses comma minus 2 pi comma alpha. Press Enter. Here, fT defines the tangent function of x.
Drag slider ϴ to 360.	Drag slider theta to 360.
Point to fT tangent function graph.	This graphs tangent function of x in the domain from minus 2 pi to alpha.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Inverse tangent function Type i_T: = Function[atan(x), -∞, ∞] in input bar >> press Enter.	In 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. Here, IT defines the inverse tangent (or arctangent) function of x.
Point to iT function graph.	This graphs the inverse tangent function of x. x lies between minus infinity and plus infinity. Observe the graph.
Point on tangent function Type P_T = (tan(α), α) in input bar >> press Enter	In input bar, type the following command: P underscore T colon is equal to Type the following words in parentheses. Tan alpha in parentheses comma alpha Press Enter.
Point to PT.	This creates point PT.
In Algebra view, right-click on PT, check Trace On option.	In Algebra view, right-click on PT, check Trace On option.
Drag slider ϴ to 360.	Drag slider theta to 360.
Point to traces of PT, iT and FT.	Traces appear for inverse tangent function graph for alpha. FT also appears in Graphics view. Compare iT and traces of PT.
Drag slider theta back to -360.	Drag slider theta back to minus 360.
Click on Move Graphics View tool and move Graphics view to erase traces of PT.	Click on Move Graphics View tool and move Graphics view to erase traces of PT.
In Algebra view, check fS, fC, iS, iC, PS and PC to show them again.	In Algebra view, check fS, fC, iS, iC, PS and PC to show them again.
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 tool. Click on the top of the grid in Graphics view.
Point to the dialog box.	Check-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 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.	Click on check box tool. Click on the top of the grid in Graphics view.
Point to the dialog box.	Check-Box to Show/Hide Objects dialog-box appears.
Type COSIN as caption.	In the Caption field, type COSIN.
Click on Objects >> select fS, iS and PS >> apply.	Click on Objects drop-down menu to select fc, ic and Pc, one by one, click Apply.
Point to check box “COSIN”.	A check-box “COSIN” is created in Graphics view. It gives us option to display or hide cosine, arccosine graphs and point Pc.
Click on check box. Click on the top of the grid in Graphics view.	Click on check box tool. Click on the top of the grid in Graphics view.
Point to the dialog box.	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 on Graphics view. It gives us option to display or hide tangent, arctangent graphs and point PT.
Click on Move tool to uncheck all boxes.	Click on Move tool to uncheck all boxes.
Check “SIN” box.	Check “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 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 “COSIN” box.	Check “COSIN” box.
Drag slider theta to 360.	Drag slider theta to 360.
Point to fC, iC and traces of PC in Graphics view.	Observe fC, iC and traces of PC appear in Graphics view.
Uncheck COSIN box.	Uncheck COSIN box.
Click on and move Graphics view slightly to erase traces of PC.	Click on and move Graphics view slightly to erase traces of PC.
Drag slider theta back to minus 360.	Drag slider theta back to minus 360.
Check “TAN” box.	Check “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 SIN and COSIN boxes.	Check SIN and COSIN boxes.
Drag slider theta to 360.	Drag slider theta to 360.
Point to all the functions in Graphics view.	Observe all the functions appearing in Graphics view.
	Let us summarize.
Slide Number 6 Summary	In this tutorial, we have learnt how to use GeoGebra to graph: Sine, cosine, tangent functions of alpha Inverse sine, cosine, tangent functions of alpha View or hide them using check-boxes
Slide Number 7 Assignment	As an assignment: Plot graphs of inverse functions of secant, cosecant and cotangent.
Slide Number 8 About Spoken Tutorial project	The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
Slide Number 9 Spoken Tutorial workshops	The Spoken Tutorial Project team conducts workshops and gives certificates. For more details, please write to us.
Slide Number 10 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 11 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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