Transformations reflected in the equation | HP 39gs Graphing

Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of y = a sin (bx + c) + d as the values of a, b, c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation.

Press , select Trig Explorer, and then press to display the screen shown right.

In this mode, the graph
In this mode, the graph
controls the equation.
Pressing the		and
	keys transforms the
graph, with these
transformations reflected in the equation.
The button labelled		is			Origin
a toggle between					Origin
a toggle between
and	. When
is chosen, the ‘point of
control’ is at the origin (0,0)
and the	and
keys control vertical and
horizontal transformations. When						is chosen the

‘point of control’ is on the first extremum of the graph (i.e. for the sine graph at (π ⁄ 2,1) .

The arrow keys change the amplitude and frequency of the graph. This is most easily seen by experimenting.

Pressing displays the equation at the top of the screen. The equation is controlled by the graph. Pressing the and keys moves from parameter to parameter. Pressing the parameter’s values.

Extremum

or key changes the

The default angle setting for this aplet is radians. The angle setting can be changed to degrees by pressing .

Getting started

1-15

Image 25

HP 39gs Graphing manual Transformations reflected in the equation

Contents

Edition3 Part Number F2223AA-90001 Users guide USA Printing HistoryEdition December June Contents 10-1 Using variables in equations10-6 11-4 11-111-8 11-9 Program constants 13-24 Physical constants 13-25 13-24Introduction 14-1 Storing and recalling variables 14-2 14-4 18-9 18-718-30 19-1 Service Regulatory information Manual conventions PrefaceHewlett Packard’s Calculators web site can be found at Function, Polar, ParametricPage Getting started On/off, cancel operationsHome Display To adjustParts of the display Contrast Menu keys KeyboardInfrared or cable Aplet library on Aplet control keysDisplays the Views menu. See Aplet views on Button performs Entry/Edit keys Shifted keystrokes Math keys Helpwith Menus CommandsProgram Inactive keys Input forms Reset input form values You use the Modes input form to set the modes for Home Mode settings Setting a mode Press to return to Home Aplets E-lessons Polar Example x = cost and y = sintSequence Sequence functions U in terms of n, or Another sequence, such as Un 1 Quad Explorer aplet Transformations reflected in the equation Press to display the aplet’s Symbolic view Symbolic view Plot viewAplet library Aplet views Select Plot-Detail Select Plot-TableSelect Overlay Plot Plot Setup Numeric Setup Symbolic Setup Aplet view configurationSketch view To save aplet configuration Where to startMathematical calculations Entering expressions Using Long results Negative numbers Scientific notation powersExplicit and implicit multiplication 23 3 EEX Entering Calculates Sin 45 + π Parentheses Input Output Last input Edit line Last output Getting started Storing a value in a variable Accessing the display history Clearing the display history Using fractionsSetting Fraction mode Setting fraction precision Select Fraction calculationsFraction Enter the calculation Evaluate the calculation Converting decimals to fractionsFraction as This example, the fraction precision is set to Complex numbers Catalogs and editors Defining an expression Symbolic view About the Symbolic viewAplets and their views Aplet views Independent variable in the expressions is T Aplets Evaluating expressionsSelect Function Home About the Plot view Setting up the plot Plot view setup ΘRNG Plot view settingsΘSTEP Exploring the graph Reset plot settings To move between relations Trace a graph To jump directly to a value To turn trace on/off Zoom within a graphZoom options Set SquareFactors Auto Scale Now un-zoom Un-zoom To box zoom Views menu options Other views for scaling and splitting the graph Split the screen Unit. Resets default values forMaking each pixel=1 unit. Not Pixel=π/24 radian, 7.58, or Decimal scaling Overlay plotsInteger scaling Trigonometric About the numeric view Setting up the table Numeric view setup Exploring the table of numbers Numeric view settingsNUM view menu keys Zoom within a table Integer Numstart and Numstep Build a table Building your own table of numbersClear data Numtype Build Your Own Example plotting a circle Build Your Own menu keys Function aplet, specify the functions Reset the graph setup to the default settingsFunction Display the functions in numeric formPage About the Function aplet Function apletGetting started with the Function aplet Open the Function aplet Plot the functions Define the expressions Set up the plotSpecify a grid for the graph Plot the functions Select Auto Change the scale Trace a graphScale Times Select Root Analyse graph with FCN functions Select Signed area Select Slope Select Extremum To find the extremum of the quadratic Explore the table Display the numeric viewDisplay the table of values Display the symbolic definition for the F1 column Symbolic definition A columnSymbolic definition F1 is displayed at Bottom of the screen To display Select Plot FCN Function aplet interactive analysisOr to choose a variable Root FCN functionsExtremum Slope Shading area Symbolic view. DisplaysIntersection Cursor. You need to have at Plotting a piecewise-defined function About the Parametric aplet Parametric apletGetting started with the Parametric aplet Define the expressions Set angle measure Set up the plot Plot the expressionSet the angle measure to degrees Select Degrees Plot a triangle graph over the existing circle graph Overlay plot Display the numbers120 Page Getting started with the Polar aplet Polar apletOpen the Polar aplet Select Polar Display the Plot view menu key labels Explore the graph Display the numbers About the Sequence aplet Sequence apletGetting started with the Sequence aplet Open the Sequence aplet Define the expression Specify plot settingsSequence Menu keys to assist in the entry of equations Plot the sequence Plot Setup, set the Seqplot option to CobwebSelect Cobweb Display the . Display the table of values for this examplePage About the Solve aplet Solve aplet Open the Solve aplet Getting started with the Solve apletDefine the equation Enter known variables Select Solve Modes is set to Comma, use instead Solve the unknown variable Plot the equation Solve aplet’s NUM view keys are Plot the equation for variable aCopies the highlighted value to Displays other pages of variables, if Use an initial guess Interpreting results Consider the equation of motion for an accelerating body Plotting to find guesses Plot the graph To highlight T Press until the cursor is at the intersection Using variables in equations Open the Linear Sequence aplet Linear Solver apletSelect Linear Solver Hence we need the three-equation input form Solver was able to find solutions for x, y, and z as Linear Solver aplet Page About the Triangle Solver aplet Triangle Solve aplet Triangle Solver Open the Triangle Solver aplet Errors Addition, you cannot specify only angles and no lengths Not enough data About the Statistics aplet Statistics apletGetting started with the Statistics aplet Select Statistics Enter dataEnter the data into the columns To move to the next column Choose fit and data columns Explore statistics Select a fit in the Symbolic setup viewValue is Display the equation for best linear fit Setup plot Plot the graph Draw the regression curveTo move to the FIT1 field Slope m is 425.875. The y-intercept b is To highlight Predict valuesStat-Two Statistics aplet’s Numeric view keys are Entering and editing statistical data Statistics Copies the column variable or Expression in standard Mathematical form. Press When DoneVariable expression to the edit line Expression Data sets will need to be selected Clear is usedAgain before re-use Plot a histogram of the data Save data Edit a data set Sort data values Delete data Insert data Defining a regression model Angle SettingTo choose the fit Fit models To define your own fit 7,8,15,16,17 Computed statistics Two-variable PlottingColumns for a linear fit only Histogram Box and Whisker Plot Plot typesTo plot statistical data Scatter Plot Fitting a curve to 2VAR dataCorrelation coefficient Relative Error Setting up the plot Plot setup viewPlotting mark 2VAR Connected points 2VAR Statistics aplet’s Plot view keys Trouble-shooting a plotErases the plot Find predicted values Calculating predicted valuesAccording to the current regression Model Statistics aplet 10-21 Page About the Inference aplet Inference apletGetting started with the Inference aplet Open the Inference aplet Inference aplet’s Symb view keys Table below summarizes the options available Symbolic view Select the inferential method Enter data Setup-NUMSelect Hypoth Test Test 1 μ Importing sample statistics from the Statistics aplet Are explained in the feature of this aplet Statistics aplet opens in the Numeric view If the Decimal Mark setting in the Modes input formC1 column, enter the random numbers Produced by the calculator 529 295 952 259 925 592 Open Inference aplet Set up the interval calculationInference Select Conf Interval Specify a 90% Confidence interval in the C field Display Numeric view Display Plot viewTo move to the C field One-Sample Z-Test Hypothesis testsMenu name Inputs Results Two-Sample Z-Test Population 2 standard One-Proportion Z-TestTest 1π Measures the strength of the evidence for a selected Two-Proportion Z-Test One-Sample T-Test With the α level that you Sample standard deviation Pooled? Two-Sample T-Test One-Sample Z-Interval Confidence intervals Two-Sample Z-Interval Two-Proportion Z-Interval One-Proportion Z-Interval One-Sample T-Interval Pooled Two-Sample T-Interval Critical T Critical value for T Background Using the Finance Solver 3 4 Compounding period -- which is PMT Performing TVM calculations Example 1 Loan calculations Example 2 Mortgage with balloon payment To calculate amortizations Calculating AmortizationsExample 3 Amortization for home mortgage To continue amortizing the loan Example 4 Amortization for home mortgage Math functions Using mathematical functionsMath menu Name. Note You do not need to press first Function categories Math functions by categorySyntax Functions common to keyboard and menus Value1+ value2 , etc Keyboard functionsEvalue E5 returns LOG100 returns Returns ABS1,2 returns Nthroot 8 returns Calculus functions∂ s1s1 2+3*s1 returns 2*s1+3 S1,2*X+3,X Taylor Complex number functionsARG Conj Conversions ConstantsMaxreal Minreal Hyperbolic trigonometry Loop functions List functions Polynomial functions Matrix functionsPolycoef Polyeval Polyroot Probability functionsComb Perm Real-number functions Floor DEG→RADFnroot Frac Mant INTMAX MIN RAD→DEG TotalRound Sign Two-variable statistics Symbolic functionsXpon Isolate Quad Test functionsQuote QUADX-12-7,X returns Ifte Trigonometry functionsNot XOR Symbolic calculations To find derivatives in Home Finding derivatives Evaluate the function Show the result To find derivatives in the Function aplet’s Symbolic viewSelect F2X and evaluate it You could also just define To find the indefinite integral using formal variablesFor example, to find the indefinite integral Program constants Program constants and physical constants Physical constants 13-26 Introduction Variables and memory management Storing and recalling variables Calculations To use variablesTo clear a variable Open the Vars menu Vars menuPress Names or values of variables into programs Add the contents of two list variables, and to storeExample Result in another list variable 14-6 To store into a graphics variable on That you can configure using17-5 for more information on X0, Y0 to X9, Y9 Symbolic view. See To access an apletVariable Aplet variables on page R-7 Line, press and press Memory ManagerDetails of variables within the category To delete variables in a categoryPage Vectors MatricesMatrices Matrix Variables Matrix Catalog keys Creating and storing matricesPOLYROOT1,0,-1,0 M1 To create a matrix in the Matrix Catalog To transmit a matrix Working with matrices Or column you are prompted to Deletes the highlighted cells, rowMake a choice Moves to the first row, last row, first To store one element Matrix arithmeticCreate the second matrix Matrices 15-7 Open the Matrix catalog and create a vector Solving systems of linear equations Select Real matrix About commands Matrix functions and commandsArgument conventions About functions Cross CondDET DOT Rank MakematRownorm Rref Examples Transposing a Matrix Reduced-Row Echelon Form Matrices 15-15 Page You can create, edit, delete, send, and receive named Lists List catalog keys List edit keys Create a list To display a list Displaying and editing listsTo display one Element To insert an element 1. Open the List catalog A listPress , and press 148 L12 Deleting lists List functionsTransmitting lists To delete a list CONCATlist1,list2 2,3 returns 5,10,15CONCAT1,2,3,4 returns 1,2,3,4 ΔLISTlist1 ΠLISTlist 23 27 Calculates the product of all elements in listΠLIST2,3,4 returns Finding statistical values for list elements 16-10 To write a note in Note view Aplet note viewYour work is automatically saved. Press any view key Or to exit the Notes view Commands Contents of variablesSpace key for text entry Alpha-lock for letter entry Sketch keys Aplet sketch viewTo draw a line Draw keys To draw a box Press to continue drawing, or press Mynote Begins a new note, and asks Opens the selected note forFor a name Another HP 39gs or PC Press instead Programming Contents of a Program Structured Programming Open Program Catalog Program catalogBe simple-or it can be divided further into other Programs that perform smaller tasks Program catalog keys Create a new program Creating and editing programsPress Progrm to open the Program catalog Press to paste the command into the program editor On the left, use or to highlight a commandEdit a program 1. Press Progrm to Editing keys Run a program Debug a program Stop a program Using programs Transmit a program Customizing an aplet Example Aplet naming convention Save the aplet Configuring the Setviews menu option programs ’’My Entry1’’’’EXP.ME1’’1 Setviews ’’’’ ’’’’18’’My Entry2’’’’EXP.ME2’’3 ’’ ’’’’EXP.SV’’0 ’’’’’’EXP.ANG’’0 Programming commands’’Start’’’’EXP.S’’7 Check Aplet commandsSelect Setviews Auto-run programs Associating programs with your aplet ViewNumber ProgramNameIncluding standard menu options Uncheck Branch commandsIF...THEN...END Uncheck n END CASE...END Iferr Then ELSE… IF... THEN... ElseEND If A==1 RUN Drawing commandsStop Erase BOXFreeze Line Graphic commands Makegrob GrobxorPLOT→ →PLOT Loop commands Matrix commands Redim RandmatScale Scaleadd Prompt commands Print commands Disp ClrvarDispxy Disp 3A is 2+2 51.52HELLO DisptimeEditmat matrixname Input GetkeyMsgbox Stat-One commands Stat-One and Stat-Two commandsStat-Two commands Storing and retrieving variables in programs Plot-view variables Hmin/Hmax GridIndep InvCross Labels IsectRecenter Root SeqPlot S1mark-S5markSimult Slope Ustep Umin/UmaxTmin / Tmax Tracing Xcross TstepYcross Ytick Yzoom Ymin / Ymax Symbolic-view variables Cubic S2fit S1fit...S5fit C1...C9, C0 Numeric-view variablesDigits Format NumFont NumColNumIndep NumRow NumType NumStepNumZoom StatMode PageNum Sketch variablesFollowing aplet variable is available in Note view Graphicname Creating new aplets based on existing aplets Extending aplets Solve Open the Solve aplet and save it under the new nameDegrees Using a customized aplet Resetting an apletChoose the sine formula in E1 Sending and receiving aplets Downloading e-lessons from the webHewlett-Packard’s Calculators web site can be found at To transmit an aplet To sort the aplet list To delete an aplet Sorting items in the aplet library menu list Glossary Reference informationExpression line# Cross matrix1,matrix2 Record using the Program editor Editor and catalog Matrix Two-dimensional array of valuesVector One-dimensional array of values Set to Comma and enclosed To erase all memory and reset defaults Resetting the HP 39gsTo reset using the keyboard If the calculator does not turn on Operating detailsBatteries To install the main batteries To install the backup battery Home variables Variables Area Root Extremum Slope Isect Function aplet variablesAngle Parametric aplet variables are Category Available name Plot Parametric aplet variables Polar aplet variables are Category Available names Plot Polar aplet variables Sequence aplet variables are Category Available name Plot Sequence aplet variables Solve aplet variables are Category Available name Plot Solve aplet variablesDigits NumCol Format NumRow Statistics aplet variables Math functions Math menu categoriesMath functions are Category Available name Calculus Hyperb Polynom Category Available name Matrix Standard Sci Fixed Eng Fraction Degrees Grads RadiansCobweb Stairstep Stat1Var Stat2Var Wavelength, λc Compt w... Compton Program commands are Category Command Aplet Program commandsBranch Print Status messages Category Command Stat-Two Function name in the index to Also be correct. Look upFind its proper syntax Function value, root, extremumPage HP 39gs Graphing Calculator Warranty period 12 months Limited WarrantyPage Service Rotc = Rest of the country Canada 905 206-4663 or Regulatory information This marking is valid for EU XxxxPage Page Branch structures 18-17 build your own table Index Contrast Freeze 18-20 Line 18-20 Pixoff 18-20 Pixon 18-20 Tline Acosh Alog Asinh Atanh Cosh EXP GroborPage Page Angle measure 1-10 decimal mark 1-11 number format Trigonometric scaling 2-14 two-variablestatistics Sending and receiving 18-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Page