Natural family

Natural Color Graphing quick reference

A color graphing calculator with natural math input. The MAIN MENU opens apps for calculating, statistics, graphing, tables and equations, and the six F keys under the screen run whatever labels the bottom bar shows. Graphs are drawn in color, with trace, zoom and solve tools.

Main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start. · Shift layer: SHIFT · Second layer: ALPHA

Open in Trident

Keys

Menus and screens

MAIN MENU (MENU)

Pick an app with the arrows and EXE, or press its number: 1 Run-Matrix, 2 Statistics, 3 Graph, 4 Table, 5 Equation. Recursion (6) is not available yet.

Run-Matrix bar

F2 DEL-H clears history, F3 MAT edits matrices A to F, F4 MATH inserts log base, abs, derivative, integral, sum and roots.

OPTN

In Run-Matrix, opens lists, matrix, complex, calculus, hyperbolic, probability, numeric and angle tools on the F keys.

VARS

In Run-Matrix, inserts graph function names Y and r.

Statistics app

Lists 1 to 6 editor. F1 GRAPH, F2 CALC (1-VAR, 2-VAR, regression), F3 TEST, F4 INTR, F5 DIST; F6 pages to DEL, DEL-ALL, INS.

Graph and Table apps

Function list: F1 SELECT, F2 DELETE, F3 TYPE, F4 TOOL (color), F6 DRAW (Graph) or SET and TABLE (Table).

Graph screen

SHIFT with F1 to F6 gives TRACE, ZOOM, V-WIN, SKETCH, G-SOLV and G⇔T (back to the list).

Equation app

F1 SIMUL (2 to 6 unknowns), F2 POLY (degree 2 to 6), F3 SOLVER for a single equation.

Modes and settings

Input/Output

SHIFT then MENU (SET UP): Math for natural display, Line for single-line entry.

Angle

Radian, degree or gradian. The start-up setting is radian.

Frac Result

Improper (d/c) or mixed (ab/c) fractions.

Complex Mode

Real only, rectangular a+bi, or polar r∠θ.

Display and Digits

Norm 1, Norm 2, Fix or Sci, with a digit count for the last two.

Graph options

Coord readout, Grid (off, on, line) and Axes on or off.

A-LOCK

SHIFT then ALPHA keeps the letter layer on until you press ALPHA again.

Tips

• The F-key labels at the bottom change with the app and menu; press SHIFT with an F key for the printed gold command.
• In Run-Matrix, starting a line with an operator uses the previous answer (Ans) automatically.
• Press S⇔D on an answer line to switch between exact and decimal form.
• Press the up arrow on an empty line to bring back a previous entry for editing.
• In the Graph app, type a function with X,θ,T, then F6 (DRAW); use SHIFT F3 (V-WIN) to set the viewing window.
• Letters need ALPHA first; store a value with the arrow key (→) and a variable letter.

Guides for this calculator

• Store a number in a variableSave a value under a letter so you can use it again in later calculations.
• Solve a quadratic equationFind the roots of x² − 5x + 6 = 0 with a polynomial solver or the quadratic formula.
• Solve a system of two equationsFind x and y when 2x + y = 5 and x − y = 1.
• Solve a system of three equationsFind x, y and z for three linked equations.
• Set degrees or radiansTell the calculator whether angles are measured in degrees or radians before you use sin, cos or tan.
• Find sine, cosine and tangentGet sin, cos or tan of an angle, here sin 50, cos 50 and tan 50 in degrees.
• Find an angle from a ratioUse the inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to turn a ratio back into an angle.
• Convert between degrees and radiansChange an angle from degrees to radians and back with the calculator.
• Solve a right triangleFind a missing side from the hypotenuse and an angle, and a missing angle from two sides.
• Use the law of sinesFind a side of any triangle when you know the opposite angle of another side and its length.
• Use the law of cosinesFind the third side of a triangle when you know two sides and the angle between them.
• Graph a sine wavePlot y = sin(x) in a trig-friendly window and find its peak at x = π ÷ 2.
• Secant, cosecant and cotangentGet sec, csc and cot by taking the reciprocal of cos, sin and tan.
• Convert between polar and rectangularTurn a point (x, y) into a distance r and an angle θ.
• Check unit circle valuesFind the exact values of sin, cos and tan at 30, 45 and 60 degrees.
• Hyperbolic functionsFind sinh, cosh and tanh with the hyperbolic menu.
• Graph a functionType an equation such as y = x² − 4 and draw its graph, then check a point on it.
• Set the graph windowChoose the x and y ranges that the graph screen shows.
• Zoom in and out of a graphUse the zoom tools to magnify a graph or bring back a standard view.
• Trace a graphMove a cursor along a curve to read its x and y values, or jump straight to a chosen x.
• Make a table of valuesList x and f(x) side by side for a function, starting wherever you like.
• Find where two graphs meetFind the point where two curves cross, such as y = x² and y = x + 2.
• Find the zeros (roots) of a graphFind where a curve crosses the x-axis. The example is y = x² − 4, with zeros at x = -2 and x = 2.
• Find a maximum or minimumFind the lowest or highest point of a curve, such as the vertex of y = x² − 2x.
• Work with logarithmsFind log base 10 of a number and undo it with 10 to a power.
• Natural logs and the number eUse ln and eˣ, the natural log and its inverse, based on e ≈ 2.71828.
• Logarithm with any baseFind a log such as log base 2 of 20 by dividing two natural logs.
• Exponential growthFind what a quantity grows to at a fixed percentage rate, and how long it takes to double.
• Complex numbersMultiply complex numbers like (3 + 4i)(1 − 2i) and find a size (modulus) such as |3 + 4i|.
• Enter and multiply matricesStore the matrix [[1, 2], [3, 4]] and multiply it by itself.
• Matrix determinant and inverseFind the determinant and inverse of [[1, 2], [3, 4]].
• Sum a sequence or seriesAdd up the first terms of a sequence, such as 1 + 3 + 5 + … + 19, which comes to 100.
• Graph parametric equationsDraw a curve from x(t) and y(t), such as a circle from cos t and sin t.
• Graph polar equationsDraw curves given as r in terms of θ, such as the three-petal rose r = 2 sin(3θ).
• Find the slope of a function at a pointGet the derivative of a function at one x value as a decimal, using the built-in derivative function.
• Find a definite integralWork out the integral of a function between two x values and get a number.
• Shade the area under a graphDraw a curve and let the graph tools find and shade the area between it and the x-axis.
• Read the slope from a graphGraph a function and move to a point to see dy/dx, the slope of the curve there.
• Find the equation of a tangent lineUse the derivative to get the slope at a point, then build the line y = m(x − a) + f(a).
• Add up a series (sigma notation)Find the sum of an expression as the counter runs from a start to an end value.
• Enter data into a listType a set of numbers into a list so you can summarise, plot or fit them.
• Find the mean and spread of one listGet the count, sum, mean and standard deviation of a list of numbers in one go.
• Summarise paired data (x and y)Get the means, spreads and cross-product sum for two lists of numbers that go together.
• Fit a straight line to dataFind the least-squares line y = ax + b that best matches a set of points.
• Fit a parabola to dataFind the curve y = ax² + bx + c that best matches points that bend.
• Find the mean, median and modeWork out the average (mean), the middle value (median) and the most common value (mode) of a list.
• Use frequencies (how many times each value occurs)Enter each value once with a count beside it instead of typing it over and over.
• Find a probability on a normal curveWork out the chance that a normally distributed value lands between two numbers.
• Find the value for a given percentileGo backwards from an area on the normal curve to the number that cuts it off.
• Binomial probabilitiesFind the chance of getting exactly a certain number of successes in a fixed number of tries.
• Poisson probabilitiesFind the chance of a certain number of events in a fixed time or space, given their average rate.
• Generate random numbersGet a random decimal between 0 and 1, or a random whole number in a range such as a dice roll.
• Count arrangements and selections (nPr and nCr)Count how many ways to arrange or choose items from a group.
• Calculate a factorialMultiply a whole number by every whole number below it, such as 6! = 720.
• Draw a scatter plotPlot paired data as dots so you can see whether a pattern is there.