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Natural Scientific 991 manual · Chapter 4 of 18

Functions

Powers, roots, logs, trigonometry and angle units, hyperbolic functions, factorials, permutations, random numbers, rounding and more.

4.1Powers, squares and roots#

x² squares the previous value, SHIFTx³x² cubes it, and x opens a power template. √ is the square root, SHIFT∛√ the cube root and SHIFT√x a root with any index. x⁻¹ gives the reciprocal.

Example 4.1

A power

  1. Type 2 to the power 10.

    2x10=
Result of the example "A power" The display shows: 2^(10) / 1024.
You should see1024
Example 4.2

Step out of an exponent

  1. Type 2³ + 1: after the 3, press right to leave the exponent.

    2x3▶+1=
Result of the example "Step out of an exponent" The display shows: 2^3+1 / 9.
You should see9
Example 4.3

A cube root

643\sqrt[3]{64}

  1. The cube root of 64.

    SHIFT∛√64=
Result of the example "A cube root" The display shows: 3√(64) / 4.
You should see4
Example 4.4

The fifth root

  1. Open the root template: type the index 5, step right, then 32.

    SHIFT√x5▶32=
Result of the example "The fifth root" The display shows: 5√(32) / 2.
You should see2
Example 4.5

Reciprocal

  1. Type 4, then the reciprocal key.

    4x⁻¹=
Result of the example "Reciprocal" The display shows: 4⁻¹ / 1/4.
You should see1/4

4.2Logarithms and exponentials#

log is base 10 and ln is base e. SHIFT10log and SHIFTeln are their inverses, 10 to a power and e to a power. log opens a template for a logarithm with any base.

Example 4.6

Log base 10

  1. log 1000.

    log1000=
Result of the example "Log base 10" The display shows: log(1000 / 3.
You should see3
Example 4.7

Log with another base

  1. Open log, type base 2, step right, type 8.

    log2▶8=
Result of the example "Log with another base" The display shows: log_2(8) / 3.
You should see3
Example 4.8

Natural log of e cubed

  1. ln, then e to the power 3.

    lnSHIFTeln3=
Result of the example "Natural log of e cubed" The display shows: ln(e^3 / 3.
You should see3
Example 4.9

Ten to a power

  1. 10 to the power 3.

    SHIFT10log3=
Result of the example "Ten to a power" The display shows: 10^3 / 1000.
You should see1000
log⁡ba=ln⁡aln⁡b\log_b a=\frac{\ln a}{\ln b}
Change of base: the log template does this for any base

4.3Sine, cosine and tangent#

Check the angle unit first: the default is degrees. See the Modes chapter to change it. Exact values such as sin 30° = 1/2 and cos 45° = √2/2 are shown exactly.

Example 4.10

Sine of 30 degrees

  1. sin 30.

    sin30=
Result of the example "Sine of 30 degrees" The display shows: sin(30 / 1/2.
You should see1/2
Example 4.11

Cosine of 45 degrees

  1. cos 45.

    cos45=
Result of the example "Cosine of 45 degrees" The display shows: cos(45 / √2/2.
You should see√2/2
Example 4.12

Tangent of 60 degrees

  1. tan 60.

    tan60=
Result of the example "Tangent of 60 degrees" The display shows: tan(60 / √3.
You should see√3
Example 4.13

Inverse sine

  1. SHIFT sin, then 1/2.

    SHIFTsin⁻¹sin1/2▶=
Result of the example "Inverse sine" The display shows: sin⁻¹(1/2 / 30.
You should see30
Example 4.14

Sine in radians

  1. Set radians (SETUP, 2 Angle Unit, 2 Radian).

    SHIFTSETUPMENU22

  2. Type sin(π/6).

    sin/SHIFTπ×10ˣ▼6=
Result of the example "Sine in radians" The display shows: sin(π/6 / 1/2.
You should see1/2
sin⁡30∘=12,cos⁡45∘=22,tan⁡60∘=3\sin 30^{\circ}=\tfrac12,\quad \cos 45^{\circ}=\tfrac{\sqrt2}{2},\quad \tan 60^{\circ}=\sqrt3
Exact trigonometric values shown by the calculator

4.4Hyperbolic functions#

Press hyp to open a menu of sinh, cosh, tanh and their inverses. Choose one with its number.

Example 4.15

The hyperbolic menu

  1. Open the menu.

    hyp
Result of the example "The hyperbolic menu" The display shows: 1:sinh / 2:cosh / 3:tanh / 4:sinh⁻¹.
You should see1:sinh 2:cosh 3:tanh
Example 4.16

cosh 1

  1. Choose 2 (cosh), type 1.

    hyp21=
Result of the example "cosh 1" The display shows: cosh(1 / 1.543080635.
You should see1.543080635
Example 4.17

Inverse sinh

  1. Choose 4 (sinh⁻¹), type 1.

    hyp41=
Result of the example "Inverse sinh" The display shows: sinh⁻¹(1 / 0.881373587.
You should see0.881373587

4.5Absolute value#

SHIFTAbshyp opens an absolute-value template. Type the value inside it.

Example 4.18

|-7|

  1. SHIFT hyp, then minus 7.

    SHIFTAbshyp(−)7=
Result of the example "|-7|" The display shows: |-7| / 7.
You should see7

4.6Factorials, permutations and combinations#

SHIFTx!x⁻¹ is the factorial. SHIFTnPr× is nPr (ordered selections) and SHIFTnCr÷ is nCr (unordered selections).

Example 4.19

5 factorial

  1. Type 5 then SHIFT x⁻¹.

    5SHIFTx!x⁻¹=
Result of the example "5 factorial" The display shows: 5! / 120.
You should see120
Example 4.20

Permutations 5P2

5P2=5!3!{}_5P_2=\frac{5!}{3!}

  1. 5, SHIFT ×, 2.

    5SHIFTnPr×2=
Result of the example "Permutations 5P2" The display shows: 5P2 / 20.
You should see20
Example 4.21

Combinations 5C2

  1. 5, SHIFT ÷, 2.

    5SHIFTnCr÷2=
Result of the example "Combinations 5C2" The display shows: 5C2 / 10.
You should see10
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

4.7Random numbers#

SHIFTRan#. types Ran#, a random decimal from 0 up to 1. ALPHARanInt. types RanInt#( for a random whole number between two limits, for example RanInt#(1,6) simulates a die. A different value appears each time.

Example 4.22

Roll a die

  1. ALPHA point, then 1, comma, 6, close the bracket.

    ALPHARanInt.1SHIFT,)6)=
Result of the example "Roll a die" The display shows: RanInt#(1,6) / 2.
You should seeRanInt#(1,6)

4.8Rounding: Int, Intg and Rnd#

Press OPTN to find the rounding tools. Int( drops the fractional part toward zero, Intg( gives the greatest whole number not above the value, and Rnd( rounds to the Fix or Sci setting in force.

FunctionExampleResult
Int(Int(-2.7)-2
Intg(Intg(-2.7)-3
Rnd(Rnd(2.718) with Fix 22.72 (stored as 68/25)
Example 4.23

Int of a negative

  1. OPTN 5 (Int), then minus 2.7.

    OPTN5(−)2.7)=
Result of the example "Int of a negative" The display shows: Int(-2.7) / -2.
You should see-2
Example 4.24

Intg of a negative

  1. OPTN 6 (Intg), then minus 2.7.

    OPTN6(−)2.7)=
Result of the example "Intg of a negative" The display shows: Intg(-2.7) / -3.
You should see-3
Example 4.25

Round to two decimals

  1. Set Fix 2 (SETUP, 3, 1, 2).

    SHIFTSETUPMENU312

  2. OPTN 7 (Rnd), type 2.718.

    OPTN72.718)=
Result of the example "Round to two decimals" The display shows: Rnd(2.718) / 68/25.
You should see68/25

4.9Greatest common divisor and least common multiple#

OPTN 8 types GCD( and OPTN 9 types LCM(. Separate the two numbers with SHIFT,) (comma).

Example 4.26

GCD of 12 and 18

  1. OPTN 8, 12, comma, 18.

    OPTN812SHIFT,)18)=
Result of the example "GCD of 12 and 18" The display shows: GCD(12,18) / 6.
You should see6
Example 4.27

LCM of 4 and 6

  1. OPTN 9, 4, comma, 6.

    OPTN94SHIFT,)6)=
Result of the example "LCM of 4 and 6" The display shows: LCM(4,6) / 12.
You should see12

4.10Convert between rectangular and polar coordinates#

SHIFTPol+ is Pol( and converts x and y to a radius and an angle. SHIFTRec− is Rec( and converts a radius and angle back to x and y. Both show their two results in braces. The angle uses the current angle unit.

Example 4.28

Pol(3, 4)

  1. SHIFT +, then 3, comma, 4.

    SHIFTPol+3SHIFT,)4)=
Result of the example "Pol(3, 4)" The display shows: Pol(3,4) / {5,53.13010235}.
You should see{5,53.13010235}
Example 4.29

Rec(2, 90)

  1. SHIFT −, then 2, comma, 90.

    SHIFTRec−2SHIFT,)90)=
Result of the example "Rec(2, 90)" The display shows: Rec(2,90) / {0,2}.
You should see{0,2}
r=x2+y2,θ=tan⁡−1yxr=\sqrt{x^2+y^2},\qquad \theta=\tan^{-1}\frac{y}{x}
What Pol( computes (Rec( reverses it)

4.11Mark a number as degrees or radians#

OPTN 2 opens an angle menu: ° (degrees), r (radians) and ►DMS. Using a mark inside an expression overrides the angle unit for that number.

Example 4.30

The angle menu

  1. OPTN then 2.

    OPTN2
Result of the example "The angle menu" The display shows: 1:° / 2:r / 3:►DMS.
You should see1:° 2:r 3:►DMS
180∘=π rad=200 grad180^{\circ}=\pi\text{ rad}=200\text{ grad}
Angle units

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