About the Parametric aplet, Enter each equation

Parametric aplet

About the Parametric aplet

The Parametric aplet allows you to explore parametric equations. These are equations in which both x and y are defined as functions of t. They take the forms x = f(t) and

y= g(t) .

Getting started with the Parametric aplet

Open the Parametric aplet

Define the expressions

The following example uses the parametric equations

x(t) = 3 sin t y(t ) = 3 cos t

Note: This example will produce a circle. For this example to work, the angle measure must be set to degrees.

1. Open the Parametric aplet.

>$3/( @ Select

Parametric

67$57_

2.Enter each equation.

3 >;@>6,1@>;75@>@ >(17(5@

3 >;@>&26@>;75@>@ >(17(5@

Parametric aplet

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HP 40G manual About the Parametric aplet, Getting started with the Parametric aplet, Enter each equation

Contents

USER’S Guide Page Contents Parametric aplet Importing Sample Statistics from the Statistics aplet Inference aplet Variables and memory management Programming Index Manual conventions Preface@, &26@, +20@, etc +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc Preface Getting started On/off, cancel operationsHome Display To adjust the contrast To clear the displayParts of the display Menu keys KeyboardAnnunciator Description Key Meaning Aplet control keys $/3+$@ +,7@175@ 75@ Helpwith Shifted keystrokesKey Description +,7@$/3+$@ Math keys Program commands Inactive keys Menus To cancel a menuTo search a menu Reset input form values Mode settingsSetting Options Input forms Setting Options Aplets E-lessons Setting a modePress+20@ to return to Home Aplet Use this aplet to explore Name N T Quad Explorer aplet *,*A, keys Trig Explorer aplet Aplet library Symbolic view Plot view Numeric viewAplet views Aplets are stored in the Aplet library Views menu contains the Plot-Table view Plot Setup Numeric Setup Symbolic Aplet view configurationConfiguration To change views Entering expressions Mathematical calculationsLong results Negative numbers Example Explicit and implicit multiplication Scientific notation powers@4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ @ 45 @6+,7@π Entering Calculates+,7@√ 85@9 +,7@√ @85 @9 @ Clearing numbers Using previous results 50175@ @25 175@175@ 175@ updates ANS from 50 to 75 to $/3+$@ a 175@ Accessing the display historyKey Function Setting Fraction mode Using fractionsSee Setting fraction precision below for more information Clearing the display history Setting fraction precision Return to Home and enter the calculation Fraction calculations Converting decimals to fractions@@@2@3 Evaluate the calculation Converting a number to a fraction Complex numbersComplex results To enter complex numbers + iy Catalogs and editors Catalog/Editor ContentsStoring complex numbers Memory manager Plot Goto function Differences between the HP 38G and the HP 39G/40GStatistics Pred function Trig Explorer and Quadratic Explorer apletsPage Defining an expression Symbolic view About the Symbolic viewAplets and their views Aplet views Aplets and their views Aplets Evaluating expressionsHome $56@ Symb view keys$7+@ +,7@CLEAR Plot view settings Setting up the plot Plot view setupAbout the Plot view 175@ or Reset plot settings Plot view keys Exploring the graph+,7@*A Zoom within a graph Trace a graphTo jump directly to a value To turn trace on/ off Zoom options Multiplies horizontal scale, using Divides horizontal scale only, usingDivides vertical scale only, using Multiplies vertical scale only, using =220Un-zoom 018ZoomPress *k, to move to the bottom of the Zoom list =220Zoom Out =220X-Zoom Out =220X-Zoom=220Y-Zoom =220Y-Zoom Out To box zoom To set zoom factors Options Other views for scaling and splitting the graph Menu key copies the right plot to the left Overlay plots About the numeric viewDecimal scaling Integer scaling Trigonometric scaling Numeric view settings Setting up the table numeric view setupReset numeric settings NUM view menu keys Exploring the table of numbersZoom within a table Arrow keys to place the cursor in the independent variable Building your own table of numbersColumn, then enter the value to jump to 175@, the values for the dependent variables are Clear data Build Your Own menu keys $3/7@ Select Example plotting a circle+,7@√@9 About the Function aplet Function apletGetting started with the Function aplet Open the Function aplet Plot the functions Define the expressions@75@175@ Plot the functions With FCN functions Change the scale Trace a graphTrace the linear function Times SelectRoot Find the greater of the two roots of the quadratic functionRoot value is displayed at the bottom of the screen Move the cursor to x = 1 by pressing the *A,or 2Select.SlopeChoose the end value for @.2 Display the numeric setup Display the numeric view Set up the tableTo find the extremum of the quadratic Display the numeric view Explore the table Match the table settings to the pixel columns in the graphDisplay a table of numeric values Move to X = Area Extremum Isect Root Slope Function aplet interactive analysis Function Description Access FCN variables FCN functions Cursor. You need to have at least Symbolic view. DisplaysTwo selected expressions =  Plotting a piecewise defined function example$3/ @ Select Page About the Parametric aplet Parametric apletGetting started with the Parametric aplet Open the Parametric aplet Define the expressions +,7@PLOT Set angle measure Set up the plot Plot the expression360 Plot a triangle graph over the existing circle graph Overlay plot Display the numbers+,7@ Plot 120Page Getting started with the polar aplet Polar apletOpen the Polar aplet +,7@CLEAR 46+,7@π 2.a Explore the graph Display the numbers Sequence aplet Sequence aplet starts in the Symbolic viewAbout the Sequence aplet Getting started with the Sequence aplet Keys to assist in the entry of equations Define the expression Plot the sequence Display the table Plot Setup, set the Seqplot option to CobwebPlot the Fibonacci sequence Select CobwebPage About the Solve aplet Solve aplet Open the Solve aplet Getting started with the Solve apletDefine the equation Define known variables Solve for the unknown variable a Solve the unknown variable Plot the equation@ Select Auto ≈20 times Solve aplet’s NUM view keys Number format Use an initial guess Message Condition Interpreting results Root- Finder at work At2 x = v0t + Plotting to find guesses$/3+$@X 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T To move cursor to the intersection Plot the graph Home variables Using variables in equationsInitial guess 3175@*k,*k,*k About the Statistics aplet Statistics apletGetting started with the Statistics aplet 1400 920 1100 2265 2890 2200 175@1 175@ 175@5 175@ 175@4 175@ Open the Statistics aplet Enter dataTo move to the next column 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Select a fit in the Symbolic setup view Choose fit and data columns Explore statistics Setup plotSelect2. Linear To move to the FIT1 +2field Display the equation for the best linear fit $7+@ S to highlight Entering and editing statistical dataTo highlight 6175@ +,7@ FXUVRU Statistics aplet’s NUM view keys 160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Before re-use Sets will need to be selected againHeight cm Frequency Save data Angle SettingDelete data Insert data Sort data values Defining a regression model 2VARTo choose the fit Select the Sort Order option. You can choose either Fit model Meaning Fit models To define your own fit= m lnx + b = ax3+bx2+cx+d. Needs at least One-variable Computed statisticsStatistic Definition Columns for a linear fit only Two-variable To plot statistical data PlottingYou can plot Histogram Box and Whisker Plot Scatter Plot Plot types Fitting a curve to0182VAR data Relative ErrorCorrelation Coefficient Plotting mark 2VAR Connected points 2VAR Setting up the plot Plot setup view Trouble-shooting a plot Statistics aplet’s Plot view keys Find predicted values Calculating predicted valuesPage Inference aplet Default the input form contains example data. This exampleAbout the Inference aplet Example data Open the Inference aplet Getting started with the Inference apletInference aplet’s Symb view keys Hypothesis Tests Confidence Intervals ∝.a∝ Define the inferential method Field name Definition Importing Sample Statistics from the Statistics aplet Open Statistics aplet. Note Reset current settingsPlot test results Open the Statistics aplet @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Calculate statistics Open Inference aplet Import the data Choose inference method and type2one.a Specify a 90% confidence interval in the C field Display Numeric view Display Plot viewE, to move to Field Display the confidence interval in the Plot view One-Sample Z-Test Hypothesis testsMenu name Inputs Results Two-Sample Z-TestResult Description One-Proportion Z-Test Successes in the two populations is equal Two-Proportion Z-TestH0 π1 = π2 Test 1 ∝ One-Sample T-TestSelected hypothesis against the null hypothesis. The null Hypothesis is that the sample mean has some assumed value Two-Sample T-Test Sample 2 standard deviation Sample 1 standard deviation Confidence interval calculations that the HP 39G/40G can Confidence intervalsPerform are based on the Normal Z-distribution or Student’s Confidence level Two-Sample Z-Interval Two populations, ∝1 ∝2, when the population standardConfidence interval for the difference between the means Deviations, σ1 and σ2, are known Sample success count One-Proportion Z-Interval Successes in two populations Two-Proportion Z-IntervalSample 1 success count Sample 2 success count One-Sample T-Interval Two-Sample T-Interval Page Math functions Using mathematical functionsMath menu Function categories To select a functionCalculus Loop Stat-Two Complex Matrices Syntax Math functions by categoryFunctions common to keyboard and menus Keyboard functions +,7@ACOS +,7@ASIN+,7@ATAN +,7@√ +,7@ABS ValuepowerABSvalue +,7@ n Taylor Calculus functionsVariableexpression Lower,upper,expression,variable ARG Complex number functionsConj Hyperbolic trigonometry Constants Alog List functionsEXP EXPM1 Matrix functions Loop functionsIterate Recurse Polycoef Polynomial functionsPolyeval Polyform Comb Probability functionsPerm Random Utpf UtpcUtpn Utpt Real-number functions →HMS HMS→INT Mant Change MODTotal RAD→DEG Sign Statistics-TwoTruncate Xpon Isolate Symbolic functionsLINEAR? Quad Quote Trigonometry functions Symbolic calculations in the Function aplet Symbolic calculationsUsing formal variables Home To find derivatives Finding derivativesGG@$/3+$@S1 Evaluate the function GG@@$/3+$@ To find derivatives in the Function aplet’s Symbolic view +,7@GG@0 @ $/3+$@ S1 @ 3 @ To find the indefinite integral using formal variablesShow the result format Thus, substituting X for S1, it can be seen that 10-26 Introduction Variables and memory management Numeric Precision Storing and recalling variablesTo store a value To store the results of a calculation To use variables Vars menuCalculations 65 @$/3+$@A 175@ +,7@LIST Names or values of variables into programs $56@ *e,*e,*e,*A 2contents,.a is copied to the command line$/3+$@L3175@ List names directly from the keyboard Category Available names Aplet variables To access an aplet variableTo copy the value of the variable into the edit line Start the Memory Manager. a list of variable categories Memory ManagerIs displayed +,7@MEMORYPage Vectors MatricesMatrices Matrix Variables Matrix Catalog keys Creating and storing matrices+ 7@CLEAR +,7@*e, or Select the type of matrix to create To create a matrix in the matrix catalog To transmit a matrix Working with matricesClears all elements from the matrix +,7@*k, *e 728 672? To multiply and divide by a scalar Matrix arithmetic175@ 2175@*e 175@ 4175@ 175@ 8 175@ $/3+$@M1 j@$/3+$@M2 175@ $/3+$@M1@ $/3+$@M2 175@ +,7@MATRIX1 175@ Solving systems of linear equations175@7 175@ +,7@MATRIX About functions Matrix functions and commands Argument conventions Eigenvv EigenvalIdenmat Inverse Rownorm RankRref Schur Trace ExamplesTRN Identity Matrix Transposing a Matrix Reduced-Row Echelon Form Creating lists ListsCreate a list in the List Catalog Open the List catalog List catalog keys List edit keys Create a list To display a list Displaying and editing listsTo display one element To edit a list @ /@ To insert an element in a list To store one element 16a*e Transmitting lists Deleting listsTo delete a list To delete all lists List functions $/3+$@L5175@ $/3+$@L 5175@ $7+@L *A$7+@L *A,Select $/3+$@A @ POSlist, element Calculates the product of all elements in listCalculates the number of elements in a list Sorts elements in ascending order 89@65@ 0@89 Finding statistical values for list elements$/3+$@ L1 175@ Go to the Numeric view To display calculated statistics 180@67$76aPage To write a note in Note view Aplet note view+,7@letter Your work is automatically saved. Press any view key +,7@ Cmds +,7@%.63$= Sketch keys Aplet sketch viewTo draw a line You can adjust the size of the box by moving the cursor Where you want any corner of the box to beTo draw a box Draw keys Press 2.again to affix the label KeysHighlight2. the variable name you want to use and press To create a note To import a graphics variable+,7@NOTEPAD Name of the note is ‘MYNOTE’ Begins a new note, and asks for Opens the selected note forTransmits the selected note to Another HP 39G/40G or PC 14-8 Programming Contents of a Program Structured Programming Open Program catalog Program catalog +,7@*k, or *e Program catalog keys Create a new program Creating and editing programs +,7@CMDS Enter commands Edit a programA,*e To enter functions more to come Editing keys Debug a program Stop a program Using programsRun a program From HOME, type RUN programname. or Copy a Working with programsProgram Transmit a program Delete a program About customizing an aplet Delete the contents of a programDelete all Programs Customizing an aplet example Aplet naming convention$3/7@Select Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Aplet commands Programming commandsCheck Select Syntax for the command is as follows Command syntax Auto-run programs Uncheck Branch commandsIF...THEN...END If test-clause IF... then Iferr trap-clause Then error-clause ENDELSE... END CASE...END Iferr Then END Drawing commands Graphic commands Grobnot →GROBGrobor Grobxor Loop commands Matrix commands Redim RandmatScale Scaleadd Prompt commands Print commands Disptime DispDisp linenumbertextitem Editmat matrixname Getkey Input nametitle,labelhelpdefaultInput Prompt MsgboxWait Wait seconds Stat-One commands Stat-One and Stat-Two commandsStat-Two commands Plot-view variables Storing and retrieving variables in programsArea Axes Extremum CoordFastRes Grid Indep HwidthInvCross Isect Recenter Nmin / NmaxRoot S1mark-S5mark Slope SimultStatPlot Umin/Umax Tracing Tmin / TmaxTstep Xcross Ytick XtickXmin / Xmax Ymin / Ymax Xzoom Symbolic-view variablesYzoom Angle R1...R9, R0 X1, Y1...X9,Y9 X0,Y0U1...U9, U0 E1...E9, E0 C1...C9, C0 Numeric-view variablesDigits NumCol FormatNumFont NumIndep NumStart NumRowNumStep NumType PageNum Creating new aplets based on existing aplets Extending aplets $/3+$@ H 175@ $1@ $/3+$@ θ @ Aplet Keys$/3+$@ C @ 175@ 180@ 35 175@ $3/ @Select Downloading e-lessons from the web Resetting an apletSolve for the missing Length of the ladder is approximately 8.72 metres To transmit an aplet Sending and receiving aplets To sort the aplet list Sorting items in the aplet library menu listTo delete an aplet Regulatory information Reference informationCanada Warranty LED safety Reference information To reset using the keyboard Resetting the HP 39G/40G If the calculator does not turn on To erase all memory and reset defaults21@ key Cross matrix1,matrix2 Glossary Operating details Operating temperature 0 to 45C 32 to 113FBatteries Home variables are Menu maps of the Vars menuCategory Available name User-named Function aplet variablesModes Function aplet variables are Plot-FCN Parametric aplet variablesParametric aplet variables are Polar aplet variables are Polar aplet variables Sequence aplet variables are Sequence aplet variables Solve aplet variables are Solve aplet variables Statistics aplet variables are Statistics aplet variablesStat-One Math functions Menu maps of the Math menuMath functions are Calculus = = Polynom Program constants Category Command Program commands Message Meaning Selected status messages+,7@ Memory Or intersection is not visible Function value, root, extremumCurrent screen Index Index Index Index Index Index Index Index Index Index Index Index Index