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Classic Scientific 30 manual · Chapter 5 of 13

Functions: logs, roots, trig, probability

Logarithms, exponentials, roots, trigonometry, hyperbolic functions, probability, rounding functions and sums.

5.1Find a logarithm or an exponential#

log⁡10(x),ln⁡(x)=log⁡e(x),10x,ex\log_{10}(x),\quad \ln(x)=\log_e(x),\quad 10^{x},\quad e^{x}
The four logarithm and exponential keys.

log is the base-10 logarithm and ln is the natural logarithm. Their 2nd functions are the opposites: 2nd10ˣlog is ten to a power and 2ndeˣln is e to a power. These templates open an exponent box, so type the power and press enter. 2nde÷ types the number e.

Example 5.1

Log base 10

  1. The log of 1000 is 3.

    log1000enter
Result of the example "Log base 10" The display shows: log(1000 / 3.
You should seelog(1000 3
Example 5.2

Ten to a power

  1. Press 2nd and log, then type the exponent.

    2nd10ˣlog3enter
Result of the example "Ten to a power" The display shows: 10^3 / 1000.
You should see10^3 1000
Example 5.3

Natural log of e squared

  1. ln of e squared is 2.

    ln2ndeˣln2enter
Result of the example "Natural log of e squared" The display shows: ln(e^2 / 2.
You should seeln(e^2 2
Example 5.4

The number e

  1. 2nd then the divide key types e.

    2nde÷enter
Result of the example "The number e" The display shows: e / 2.718281828.
You should see2.718281828

See also Work with logarithmsNatural logs and the number eLogarithm with any base

5.2Roots, cube roots and absolute value#

For an x-th root press 2ndˣ√^. Type the root number (3 for a cube root), press ▶, then type the number under the root. For a square root use 2nd√x². Absolute value is 2ndabsx⁻¹, which opens bars you fill in.

Example 5.5

Cube root of 27

  1. Press 2nd and the power key, type 3, step right, type 27.

    2ndˣ√^3▶27enter
Result of the example "Cube root of 27" The display shows: 3√(27) / 3.
You should see3√(27) 3
Example 5.6

Absolute value

  1. The absolute value of -7 is 7.

    2ndabsx⁻¹(−)7enter
Result of the example "Absolute value" The display shows: |-7| / 7.
You should see|-7| 7

See also Cube roots and other rootsAbsolute value

5.3Find sine, cosine and tangent#

sin⁡ 30∘=12,sin⁡ 60∘=32,tan⁡ 45∘=1\sin\,30^\circ=\frac12,\quad \sin\,60^\circ=\frac{\sqrt3}{2},\quad \tan\,45^\circ=1
Exact values the calculator recognises.

Sine, cosine and tangent open a bracket for you: type the angle and press enter. They use the angle unit in MODE (degrees at the start). Nice angles give exact answers in degree mode and in radian mode when you enter them with pi.

Example 5.7

Sine of 30 degrees

  1. In degree mode the sine of 30 is exactly one half.

    sin30)enter
Result of the example "Sine of 30 degrees" The display shows: sin(30) / 1/2.
You should seesin(30) 1/2
Example 5.8

Sine of 60 degrees

  1. The sine of 60 is a root, kept exact.

    sin60)enter
Result of the example "Sine of 60 degrees" The display shows: sin(60) / √3/2.
You should see√3/2
Example 5.9

Tangent of 45 degrees

  1. The tangent of 45 is 1.

    tan45)enter
Result of the example "Tangent of 45 degrees" The display shows: tan(45) / 1.
You should seetan(45) 1
Example 5.10

Sine in radians with pi

  1. Change to radians, clear, then find the sine of pi over 6.

    mode▶enterclearsinn/dπ▼6▶)enter
Result of the example "Sine in radians with pi" The display shows: sin(π/6) / 1/2.
You should see1/2

See also Find sine, cosine and tangentSet degrees or radians

5.4Find an angle from a ratio#

The inverse functions are the 2nd functions of sin, cos and tan. The answer comes in the current angle unit.

Example 5.11

Angle whose sine is 0.5

  1. Inverse sine of 0.5 is 30 degrees.

    2ndsin⁻¹sin0.5)enter
Result of the example "Angle whose sine is 0.5" The display shows: sin⁻¹(0.5) / 30.
You should seesin⁻¹(0.5) 30
Example 5.12

Inverse tangent of 1

  1. The angle with tangent 1 is 45.

    2ndtan⁻¹tan1)enter
Result of the example "Inverse tangent of 1" The display shows: tan⁻¹(1) / 45.
You should see45
Example 5.13

Inverse sine in radians

  1. In radian mode sin⁻¹(1) is pi over 2.

    mode▶enterclear2ndsin⁻¹sin1)enter
Result of the example "Inverse sine in radians" The display shows: sin⁻¹(1) / π/2.
You should seeπ/2

See also Find an angle from a ratio

5.5Hyperbolic functions#

The HYP menu (2nd then pi). The display shows: HYP / 1:sinh( / 2:cosh( / 3:tanh(.
The HYP menu (2nd then pi).

Press 2ndhypπ (HYP) to open a menu of sinh, cosh, tanh and their inverses. Press the number of the item you want, type the value and close the bracket.

NumberFunction
1sinh(
2cosh(
3tanh(
4sinh⁻¹(
5cosh⁻¹(
6tanh⁻¹(
Example 5.14

Hyperbolic sine of 1

  1. Open HYP, choose 1 (sinh), type 1 and close the bracket.

    2ndhypπ11)enter
Result of the example "Hyperbolic sine of 1" The display shows: sinh(1) / 1.175201194.
You should seesinh(1) 1.175201194
Example 5.15

Inverse hyperbolic sine

  1. Choose item 4, sinh⁻¹.

    2ndhypπ41)enter
Result of the example "Inverse hyperbolic sine" The display shows: sinh⁻¹(1) / 0.881373587.
You should see0.881373587

See also Hyperbolic functions

5.6Permutations, combinations and factorials#

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.
The PRB menu. The display shows: [PRB] RAND / 1:nPr / 2:nCr / 3:!.
The PRB menu.

Press prb for the PRB menu. Type the first number before you open the menu, then choose nPr, nCr or ! and type the second number. A factorial can also be typed with 2nd!×. If r is larger than n, nPr and nCr give 0. Negative or non-whole numbers give a DOMAIN error.

Example 5.16

Combinations

  1. Choose 2 out of 5: type 5, open PRB, pick nCr, type 2.

    5prb22enter
Result of the example "Combinations" The display shows: 5 nCr 2 / 10.
You should see5 nCr 2 10
Example 5.17

Permutations

  1. Arrange 2 out of 5.

    5prb12enter
Result of the example "Permutations" The display shows: 5 nPr 2 / 20.
You should see5 nPr 2 20
Example 5.18

Factorial

  1. 5 factorial, from the PRB menu.

    5prb3enter
Result of the example "Factorial" The display shows: 5! / 120.
You should see5! 120
Example 5.19

Factorial from the 2nd key

  1. 2nd then the times key also gives the factorial sign.

    52nd!×enter
Result of the example "Factorial from the 2nd key" The display shows: 5! / 120.
You should see120

See also Count arrangements and selections (nPr and nCr)Calculate a factorial

5.7Random numbers#

The RAND tab of the PRB menu. The display shows: PRB [RAND] / 1:rand / 2:randint(.
The RAND tab of the PRB menu.

Open the RAND tab of PRB (press prb then ▶). rand gives a random decimal between 0 and 1. randint( gives a random whole number between two limits that you type separated by a comma (2nd,.). The numbers change every time.

Example 5.20

Random decimal

  1. Open PRB, move to the RAND tab and pick rand.

    prb▶1enter
Result of the example "Random decimal" The display shows: rand / 0.2664292087.
You should seerand
Example 5.21

Roll a die

  1. Pick randint(, type 1, comma, 6 and close the bracket.

    prb▶212nd,.6)enter
Result of the example "Roll a die" The display shows: randint(1,6) / 2.
You should seerandint(1,6)

See also Generate random numbers

5.8Round, absolute value, parts of a number#

The NUM tab of the MATH menu. The display shows: MATH [NUM] CPX / 1:abs( / 2:round( / 3:iPart(.
The NUM tab of the MATH menu.

The NUM tab of the MATH menu (math then ▶) holds these functions. Pick one by its number, type the value (and a comma 2nd,. before a second value), then close the bracket.

NumberFunctionWhat it does
1abs(Absolute value.
2round(Rounds to a number of decimals: round(3.14159,2).
3iPart(Integer part: drops the decimals.
4fPart(Fractional part: keeps only the decimals.
5int(The greatest integer not larger than the number (rounds down).
6min(The smaller of two numbers.
7max(The larger of two numbers.
8mod(The remainder after division.
Example 5.22

Round to 2 decimals

  1. NUM tab, item 2, then 3.14159, comma, 2.

    math▶23.141592nd,.2)enter
Result of the example "Round to 2 decimals" The display shows: round(3.14159,2) / 3.14.
You should seeround(3.14159,2) 3.14
Example 5.23

Fractional part

  1. Item 4 keeps only the decimals.

    math▶43.7)enter
Result of the example "Fractional part" The display shows: fPart(3.7) / 0.7.
You should seefPart(3.7) 0.7
Example 5.24

Round down (int)

  1. int of -2.5 is -3, because it rounds down.

    math▶5(−)2.5)enter
Result of the example "Round down (int)" The display shows: int(-2.5) / -3.
You should see-3
Example 5.25

Integer part

  1. iPart drops the decimals, so -2.5 becomes -2.

    math▶3(−)2.5)enter
Result of the example "Integer part" The display shows: iPart(-2.5) / -2.
You should see-2
Example 5.26

Remainder

  1. 17 divided by 5 leaves 2.

    math▶8172nd,.5)enter
Result of the example "Remainder" The display shows: mod(17,5) / 2.
You should seemod(17,5) 2
Example 5.27

Smaller of two numbers

  1. Item 6 is min.

    math▶642nd,.7)enter
Result of the example "Smaller of two numbers" The display shows: min(4,7) / 4.
You should seemin(4,7) 4

5.9Find the gcd and lcm#

The MATH menu: items 1 to 6 are fraction tools, lcm, gcd, Σ, Π and F◄►D. The display shows: [MATH] NUM CPX / 1:►n/d◄►Un/d / 2:lcm( / 3:gcd(.
The MATH menu: items 1 to 6 are fraction tools, lcm, gcd, Σ, Π and F◄►D.

The MATH tab of the MATH menu has lcm( (item 2) and gcd( (item 3). Type the two numbers separated by a comma.

Example 5.28

Greatest common divisor

  1. gcd of 12 and 8.

    math3122nd,.8)enter
Result of the example "Greatest common divisor" The display shows: gcd(12,8) / 4.
You should seegcd(12,8) 4
Example 5.29

Least common multiple

  1. lcm of 24 and 6.

    math2242nd,.6)enter
Result of the example "Least common multiple" The display shows: lcm(24,6) / 24.
You should seelcm(24,6) 24

See also Greatest common divisor and least common multiple

5.10Add up or multiply a series (Σ and Π)#

∑x=110x=55,∏x=15x=120\sum_{x=1}^{10} x = 55,\qquad \prod_{x=1}^{5} x = 120
What the Σ and Π templates compute.

MATH items 4 and 5 are Σ( (sum) and Π( (product). A template opens with three boxes: the expression to add (use x as the variable), the starting value and the ending value. Move between the boxes with ▶.

Example 5.30

Sum the numbers 1 to 10

  1. Pick Σ(, type x with the variable key, move right, type 1, move right, type 10.

    math4x yzt abcd▶1▶10enter
Result of the example "Sum the numbers 1 to 10" The display shows: Σ(x,1,10) / 55.
You should seeΣ(x,1,10) 55
Example 5.31

Multiply the numbers 1 to 5

  1. Pick Π( the same way.

    math5x yzt abcd▶1▶5enter
Result of the example "Multiply the numbers 1 to 5" The display shows: Π(x,1,5) / 120.
You should seeΠ(x,1,5) 120

See also Sum a sequence or series

TI-30XS MultiView is a trademark of Texas Instruments Incorporated. Trident Calculator is an independent product by South View Studios and is not affiliated with, sponsored by or endorsed by Texas Instruments. The name is used only to describe the kind of calculator this model resembles; Trident's names, keys, display, fonts and software are its own clean-room design.