Expansion and factoring using trigonometric functions | HP 50g

Information and examples on these commands are available in the help facility of the calculator. For example, the description of EXPLN is shown in the left-hand side, and the example from the help facility is shown to the right:

Expansion and factoring using trigonometric functions

The TRIG menu, triggered by using ‚Ñ, shows the following functions:

These functions allow to simplify expressions by replacing some category of trigonometric functions for another one. For example, the function ACOS2S allows to replace the function arccosine (acos(x)) with its expression in terms of arcsine (asin(x)).

Description of these commands and examples of their applications are available in the calculator’s help facility (IL@HELP). The user is invited to explore this facility to find information on the commands in the TRIG menu.

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HP 50g manual Expansion and factoring using trigonometric functions

Contents

User’s manual HP 50g graphing calculator Printing History Preface Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Calculus Applications Graphics Probability Distributions Multi-variateCalculus ApplicationsVector Analysis Applications Differential Equations Equation Library Using SD cardsStatistical Applications Numbers in Different Bases Basic Operations Chapter Getting startedBatteries Page Menus Contents of the calculator’s displayTool menu Introducing the calculator’s keyboard Setting time and date ALPHA-Left-Shift function, to enter the lower-case letter p Selecting calculator modes √ 3.*5.-1/3.*3./23.3+EXP2.5 Operating ModePage Lets try now the expression proposed earlier Standard format Number Format and decimal dot or commaFixed format with decimals Scientific format Engineering format Decimal comma vs. decimal point Coordinate System Angle Measure Selecting CAS settings Explanation of CAS settings Selecting Display modes Selecting properties of the line editor Selecting the display font Selecting properties of the Stack Selecting properties of the equation writer EQW References Creating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stackPage Page 2L 1 + + 2 L + y Creating algebraic expressions Using the Equation Writer EQW to create expressions + 2 ⋅ 5 + ⎛ x + 2 ∝ ⋅ ∆y ⎞ Home directory Organizing data in the calculator Subdirectories VariablesTyping variable names Creating variables Algebraic mode RPN mode Page Checking variables contents Using function Purge in the stack in Algebraic mode Listing the contents of all variables in the screenDeleting variables Using function Purge in the stack in RPN mode Choose boxes vs. Soft Menu Undo and CMD functions @@OK@@ References Examples of real number calculations Chapter Calculations with real numbersPage Using powers of 10 in entering data Page Real number functions in the MTH menu Using calculator menusHyperbolic functions and their inverses Page Units menu Operations with unitsPage Attaching units to numbers Available units Unit prefixes Operations with units Unit conversions Quit Physical constants in the calculatorPage Defining and using functions Reference Chapter Calculations with complex numbers Setting the calculator to Complex modeDefinitions Entering complex numbers Polar representation of a complex number Cmplx menus Simple operations with complex numbersCmplx menu through the MTH menu Forms the complex number x,y out of real numbers x Cmplx menu in keyboard Functions applied to complex numbers Function Droite equation of a straight line Page Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Functions in the ALG menu Collect Operations with transcendental functions Expansion and factoring using log-exp functions Expansion and factoring using trigonometric functions FACTORSSIMP2 Functions in the Arithmetic menu Pcoef function PolynomialsHorner function Variable Peval function FractionsProot function Quot and Remainder functions Fcoef function SIMP2 functionPropfrac function Partfrac function Froots function Step-by-step operations with polynomials and fractions− 5X 2 + 3X − Reference Symbolic solution of algebraic equations Chapter Solution to equationsFunction Isol Function Solve Page Function Zeros Function Solvevx Numerical solver menu Polynomial Equations Finding the solutions to a polynomial equation Enter vector of roots Generating an algebraic expression for the polynomial Financial calculations Function Steq Solving equations with one unknown through Solution to simultaneous equations with Mslv Reference Page Changing sign Chapter Operations with listsCreating and storing lists Operations with lists of numbers Addition, subtraction, multiplication, division Page Functions applied to lists Lists of complex numbers MTH/LIST menu Lists of algebraic objectsPage MAP function SEQ functionPage Entering vectors Chapter VectorsTyping vectors in the stack Storing vectors into variables in the stack Moving to the right vs. moving down in the Matrix Writer Using the Matrix Writer Mtrw to enter vectors Press @GOTO@ 3@@OK@@ 3@@OK@@ @@OK@@ to move to position 3,3 Addition, subtraction Simple operations with vectors Multiplication by a scalar, and division by a scalar MTH/VECTOR menuAbsolute value function Dot product MagnitudeCross product Reference Chapter Matrices and linear algebra Using the Matrix WriterEntering matrices in the stack Typing in the matrix directly into the stack Operations with matrices Multiplication Addition and subtractionMultiplication by a scalar Matrix multiplication Matrix-vector multiplicationCij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Term-by-term multiplication Raising a matrix to a real power Inverse matrix Identity matrix TrA = ∑aii Characterizing a matrix The matrix Norm menuFunction DET Function Trace Using the numerical solver for linear systems Solution of linear systems ⎢x2 = ⎢1 Solution by division of matrices Solution with the inverse matrix References Graphs options in the calculator Chapter Graphics = 1 exp− x Plotting an expression of the form y = fxPage Generating a table of values for a function Fast 3D plots Keep the default plot window ranges to read Reference Page Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivatives Lim f Xdx = F x + C Anti-derivatives and integralsFunctions Deriv and Dervx Functions INT, INTVX, RISCH, Sigma and Sigmavx Definite integrals Functions TAYLR, TAYLR0, and Series Infinite series= ∑ Reference Partial derivatives Chapter Multi-variate Calculus Applications Multiple integrals Del operator Chapter Vector Analysis ApplicationsGradient Curl Divergence Function Ldec Solution to linear and non-linear equationsChapter Differential Equations CALC/DIFF menuPage Variable Odetype Function Desolve Laplace transform and inverses in the calculator Laplace Transforms 2inπt Fourier seriesFunction Fourier Lf t= F s = 0∞ f t ⋅ e− st dt Fourier series for a quadratic function Reference Page − r + Chapter Probability DistributionsMTH/PROBABILITY.. sub-menu part Factorials, combinations, and permutations Random numbers Normal distribution MTH/PROB menu partStudent-t distribution F distribution Chi-square distribution Entering data Chapter Statistical Applications Sample vs. population Calculating single-variable statistics Obtaining frequency distributions Page 195238095238 + 2.00857242857*X Correlation Covariance Fitting data to a function y = fx Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Page Base menu Chapter Numbers in Different Bases Writing non-decimal numbers Inserting and removing an SD card Chapter Using SD cardsFormatting an SD card Storing objects on the SD card Accessing objects on an SD card Purging an object from the SD card Recalling an object from the SD card Specifying a directory on an SD card Purging all objects on the SD card by reformatting `#EQLIB #EQNLI Chapter Equation Library Step 30 ##¢0#- L *!!!!!!V0!!!!!+ Reference Limited Warranty W-2 Europe Asia Pacific Country Telephone numbers Service America Country Telephone numbers Federal Communications Commission Notice Regulatory information Canadian Notice Korean Notice