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Natural Color Graphing manual · Chapter 4 of 18

Functions and the OPTN and MATH bars

Trigonometry, hyperbolic, probability, numeric functions, calculus, lists and angle tools.

4.1Sine, cosine, tangent and inverses#

The calculator starts in radians. For angles in degrees change the angle unit first (see Modes). Exact trigonometric values are shown exactly.

sin⁡π6=12,cos⁡π3=12,tan⁡π4=1\sin\frac{\pi}{6}=\frac12,\qquad \cos\frac{\pi}{3}=\frac12,\qquad \tan\frac{\pi}{4}=1
Exact values in radians
Example 4.1

sin(π/6) in radians

  1. sin, π, divided by 6.

    sinSHIFTπ×10ˣ÷6)EXE
Result of the example "sin(π/6) in radians" The display shows: sin(π÷6) / 1/2 / · DEL-H MAT MATH · ·.
You should see1/2
Example 4.2

tan(π/4)

  1. tan, π divided by 4.

    tanSHIFTπ×10ˣ÷4)EXE
Result of the example "tan(π/4)" The display shows: tan(π÷4) / 1 / · DEL-H MAT MATH · ·.
You should see1
Example 4.3

Inverse sine

  1. SHIFT sin, then 1.

    SHIFTsin⁻¹sin1EXE
Result of the example "Inverse sine" The display shows: sin⁻¹(1 / π/2 / · DEL-H MAT MATH · ·.
You should seeπ/2
Example 4.4

Inverse cosine

  1. SHIFT cos, then -1/2.

    SHIFTcos⁻¹cos(−)1/2EXE
Result of the example "Inverse cosine" The display shows: cos⁻¹(-1/2 / 2π/3 / · DEL-H MAT MATH · ·.
You should see2π/3
Example 4.5

sin 30 in degrees

  1. Switch to degrees (SET UP, Angle, Deg).

    SHIFTSET UPMENU▼▼F2EXIT

  2. sin 30.

    sin30EXE
Result of the example "sin 30 in degrees" The display shows: sin(30 / 1/2 / · DEL-H MAT MATH · ·.
You should see1/2

4.2The MATH bar: log base, abs, calculus#

Press F4 (MATH) for templates. The second page (F6) holds the nth root and the mixed fraction.

F keyLabelInserts
F1logabLogarithm with any base.
F2AbsAbsolute value.
F3d/dxDerivative at a point.
F4∫dxDefinite integral.
F5Σ(Summation.
F6 then F1ⁿ√Nth root.
Example 4.6

Log base 2

log⁡28\log_2 8

  1. MATH, logab, base 2, step right, 8.

    F4F12▶8EXE
Result of the example "Log base 2" The display shows: log_2(8) / 3 / logab Abs d/dx ∫dx Σ( ▷.
You should see3
Example 4.7

Absolute value

  1. MATH, Abs, then -7.

    F4F2(−)7EXE
Result of the example "Absolute value" The display shows: |-7| / 7 / logab Abs d/dx ∫dx Σ( ▷.
You should see7
Example 4.8

Slope at a point

ddxx2∣x=3\left.\frac{d}{dx}x^2\right|_{x=3}

  1. MATH, d/dx, X squared, step right, 3.

    F4F3X,θ,Tx²▶3EXE
Result of the example "Slope at a point" The display shows: d/dx(X²,3) / 6 / logab Abs d/dx ∫dx Σ( ▷.
You should see6
Example 4.9

A definite integral

∫01x2 dx\int_0^1 x^2\,dx

  1. MATH, integral, X squared, limits 0 and 1.

    F4F4X,θ,Tx²▶0▶1EXE
Result of the example "A definite integral" The display shows: ∫(X²,0,1) / 1/3 / logab Abs d/dx ∫dx Σ( ▷.
You should see1/3
Example 4.10

A sum

∑x=110x\sum_{x=1}^{10}x

  1. MATH, Σ, X, from 1 to 10.

    F4F5X,θ,T▶1▶10EXE
Result of the example "A sum" The display shows: Σ(X,1,10) / 55 / logab Abs d/dx ∫dx Σ( ▷.
You should see55
Example 4.11

Nth root from page 2

  1. MATH, next page, nth root: index 3, then 64.

    F4F6F13▶64EXE
Result of the example "Nth root from page 2" The display shows: 3√(64) / 4 / ⁿ√ a⌟b/c · · · ▷.
You should see4

4.3The OPTN bar#

Press OPTN in Run-Matrix. Choose a group with an F key, then an item. EXIT goes back one bar.

F keyGroupContains
F1LISTList, Dim, Sum, Mean, Med, Prod, Min, Max
F2MATMatA to MatF, Det, Trn, Iden, Ref, Rref
F3CPLXi, Abs, Arg, Conjg, ReP, ImP
F4CALCd/dx, ∫dx, Σ(, logab
F5HYPRBLsinh, cosh, tanh and inverses
F6 then F1PROBx!, nPr, nCr, Ran#, RanInt
F6 then F2NUMRICAbs, Int, Frac, Rnd, Intg, GCD, LCM
F6 then F3ANGLE°, r, Pol(, Rec(
OPTN then MAT lists the matrix tools The display shows: MatA MatB MatC Det Trn ▷.
OPTN then MAT lists the matrix tools
Example 4.12

Integral from the CALC group

  1. OPTN, CALC, ∫dx; 2X from 0 to 3.

    OPTNF4F22X,θ,T▶0▶3EXE
Result of the example "Integral from the CALC group" The display shows: ∫(2X,0,3) / 9 / d/dx ∫dx Σ( logab · ·.
You should see9
Example 4.13

Back out of a bar

  1. OPTN, MAT, then EXIT twice.

    OPTNF2EXITEXIT
Result of the example "Back out of a bar" The display shows: · DEL-H MAT MATH · ·.
You should seeMATH

4.4Factorials, permutations and combinations#

nPr=n!(n−r)!,nCr=n!r! (n−r)!{}_nP_r=\frac{n!}{(n-r)!},\qquad {}_nC_r=\frac{n!}{r!\,(n-r)!}
Permutations and combinations
Example 4.14

5 factorial

  1. 5, OPTN, next page, PROB, x!.

    5OPTNF6F1F1EXE
Result of the example "5 factorial" The display shows: 5! / 120 / x! nPr nCr Ran# RanInt ·.
You should see120
Example 4.15

5P2

  1. 5, PROB, nPr, 2.

    5OPTNF6F1F22EXE
Result of the example "5P2" The display shows: 5P2 / 20 / x! nPr nCr Ran# RanInt ·.
You should see20
Example 4.16

5C2

  1. 5, PROB, nCr, 2.

    5OPTNF6F1F32EXE
Result of the example "5C2" The display shows: 5C2 / 10 / x! nPr nCr Ran# RanInt ·.
You should see10

4.5Rounding, GCD and LCM#

NUMRIC: Int drops the fraction toward zero, Intg gives the greatest whole number not above, Frac the fractional part, Rnd rounds to the Fix or Sci setting.

Example 4.17

Int of a negative number

  1. OPTN, next page, NUMRIC, Int, -3.7.

    OPTNF6F2F2(−)3.7EXE
Result of the example "Int of a negative number" The display shows: Int -3.7 / -3 / Abs Int Frac Rnd Intg ▷.
You should see-3
Example 4.18

GCD

  1. NUMRIC, page 2 for GCD; 12 and 18.

    OPTNF6F2F6F112,18EXE
Result of the example "GCD" The display shows: GCD(12,18 / 6 / GCD LCM · · · ▷.
You should see6

4.6Hyperbolic functions#

OPTN then HYPRBL (F5) lists sinh, cosh, tanh and their inverses.

Example 4.19

sinh 0

  1. OPTN, HYPRBL, sinh, 0.

    OPTNF5F10EXE
Result of the example "sinh 0" The display shows: sinh(0 / 0 / sinh cosh tanh sinh⁻¹ cosh⁻¹ tanh⁻¹.
You should see0

4.7Lists in a calculation#

Braces make a list: SHIFT{× opens one and SHIFT}÷ closes it. Arithmetic works on every element. The LIST group has Sum, Mean, Med, Min and more.

Example 4.20

Multiply a list

  1. {1, 2} × 3.

    SHIFT{×1,2SHIFT}÷×3EXE
Result of the example "Multiply a list" The display shows: {1,2}×3 / {3,6} / · DEL-H MAT MATH · ·.
You should see{3,6}
Example 4.21

Sum of a list

  1. OPTN, LIST, Sum, {1,2,3}.

    OPTNF1F3SHIFT{×1,2,3SHIFT}÷EXE
Result of the example "Sum of a list" The display shows: Sum {1,2,3} / 6 / List Dim Sum Mean Med ▷.
You should see6
Example 4.22

Mean of a list

  1. OPTN, LIST, Mean, {2,4}.

    OPTNF1F4SHIFT{×2,4SHIFT}÷EXE
Result of the example "Mean of a list" The display shows: Mean({2,4} / 3 / List Dim Sum Mean Med ▷.
You should see3

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