RPN Power 48 manual · Chapter 6 of 19

Functions

Logarithms, trigonometry, hyperbolic functions, rounding, combinations and other MTH menu commands.

6.1Logarithms and exponentials#

Right shift SIN is LOG (base 10) and right shift yˣ is LN (natural). Right shift COS is ALOG (10 to the power x) and left shift yˣ is EXP (e to the power x).

Example 6.1

Common logarithm of 100

\log_{10}100=2

Type 100 and press right shift SIN.
100▶LOGSIN

Result of the example "Common logarithm of 100" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 2. — You should see`1: 2`

Example 6.2

Ten to the power 3

Type 3 and press right shift COS.
3▶10ˣCOS

Example 6.3

e to the power 1

Type 1 and press left shift power key.
1◀eˣyˣ

Example 6.4

Natural logarithm of 1

Type 1 and press right shift power key.
1▶LNyˣ

6.2Sine, cosine and tangent#

Trigonometric functions use the angle unit shown in the status line. The default is radians, so change to degrees in the MODE menu when you work with degrees. The left shift keys give the inverse functions.

Example 6.5

Sine of 30 degrees

Open MODE and press DEG (fifth key).
MODEF5
Type 30 and press SIN.
30SIN

Example 6.6

Sine of 30 radians

The default angle unit is radians.
30SIN

Example 6.7

Angle whose sine is 0.5

\sin^{-1}(0.5)=\frac{\pi}{6}

Left shift SIN is the inverse sine. In radians this gives about 0.5236.
0.5◀ASINSIN

Result of the example "Angle whose sine is 0.5" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: .523598775598. — You should see`1: .523598775598`

Example 6.8

Inverse tangent of 1 in degrees

Switch to DEG.
MODEF5
Left shift TAN of 1: 45.
1◀ATANTAN

6.3Find the hypotenuse of a right triangle#

c=\sqrt{a^{2}+b^{2}}

Example 6.9

Legs 3 and 4

\sqrt{3^2+4^2}=5

Square each leg, add, take the square root.
3◀x²√x4◀x²√x+√x

Result of the example "Legs 3 and 4" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 5. — You should see`1: 5`

6.4The MTH menu#

Left shift APPS opens MTH. It has five pages.

MTH page 1: ABS, SIGN, IP, FP, FLOOR, CEIL. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / ABS SIGN IP FP FLOOR CEIL . — MTH page 1: ABS, SIGN, IP, FP, FLOOR, CEIL.

MTH page 2: MOD, MIN, MAX, %, %T, %CH. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / MOD MIN MAX % %T %CH . — MTH page 2: MOD, MIN, MAX, %, %T, %CH.

MTH page 3: !, COMB, PERM, XROOT, RND, INV. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / ! COMB PERM XROOT RND INV . — MTH page 3: !, COMB, PERM, XROOT, RND, INV.

MTH page 4: the hyperbolic functions. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / SINH COSH TANH ASINHACOSH ATANH. — MTH page 4: the hyperbolic functions.

MTH page 5: LNP1, EXPM, D→R, R→D, MAXR, MINR. The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: / LNP1 EXPM D→R R→D MAXR MINR . — MTH page 5: LNP1, EXPM, D→R, R→D, MAXR, MINR.

Command	What it does
ABS	Absolute value (for a vector or complex number, its length).
SIGN	Sign: -1, 0 or 1.
IP, FP	Integer part and fractional part.
FLOOR, CEIL	Round down or up to a whole number.
MOD	Remainder of level 2 divided by level 1.
MIN, MAX	The smaller or larger of two numbers.
%, %T, %CH	Percent, percent of total, percent change.
!	Factorial.
COMB, PERM	Combinations and permutations of n things taken r at a time.
XROOT	The x-th root of y.
RND	Rounds level 2 to the number of digits in level 1.
INV	Reciprocal.
SINH … ATANH	Hyperbolic functions and their inverses.
LNP1, EXPM	ln(1+x) and e^x − 1, accurate for tiny x.
D→R, R→D	Degrees to radians and back.
MAXR, MINR	The largest and smallest real numbers the calculator can hold.

Example 6.10

Absolute value

Type 5, change sign, open MTH and press ABS (first key).
5+/−◀MTHAPPSF1

Example 6.11

Sign of a negative number

SIGN is the second key.
5+/−◀MTHAPPSF2

Example 6.12

Integer part

IP is the third key.
2.4567◀MTHAPPSF3

Example 6.13

Fractional part

FP is the fourth key.
2.5◀MTHAPPSF4

Example 6.14

Floor and ceiling

FLOOR (fifth key) of 2.7.
2.7◀MTHAPPSF5

Example 6.15

Round up with CEIL

CEIL is the sixth key.
2.1◀MTHAPPSF6

Example 6.16

Remainder 7 mod 3

Enter 7 and 3, then MOD (page 2, first key).
7ENTER3◀MTHAPPSNXTF1

Example 6.17

Larger of two numbers

MAX is the third key on page 2.
3ENTER9◀MTHAPPSNXTF3

Example 6.18

Smaller of two numbers

MIN is the second key on page 2.
3ENTER9◀MTHAPPSNXTF2

Example 6.19

Round to 2 digits

Type the number, then 2, then RND (page 3, fifth key).
3.14159ENTER2◀MTHAPPSNXTNXTF5

6.5Factorial, combinations and permutations#

\binom{n}{r}=\frac{n!}{r!(n-r)!},\qquad {}_nP_r=\frac{n!}{(n-r)!}

Example 6.20

Factorial of 5

5!=120

Type 5 and press left shift 3.
5◀!3

Result of the example "Factorial of 5" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 120. — You should see`1: 120`

Example 6.21

Combinations of 5 taken 2

\binom{5}{2}=10

Open MTH page 3 and press COMB (second key).
5ENTER2◀MTHAPPSNXTNXTF2

Result of the example "Combinations of 5 taken 2" The display shows: RAD { HOME } / 6: / 5: / 4: / 3: / 2: / 1: 10 / ! COMB PERM XROOT RND INV . — You should see`1: 10`

Example 6.22

Permutations of 5 taken 2

PERM is the third key.
5ENTER2◀MTHAPPSNXTNXTF3

6.6Hyperbolic functions#

\sinh x=\frac{e^{x}-e^{-x}}{2}

Example 6.23

Hyperbolic sine of 0

SINH is the first key on MTH page 4.
0◀MTHAPPSNXTNXTNXTF1

Example 6.24

Hyperbolic cosine of 0

COSH is the second key.
0◀MTHAPPSNXTNXTNXTF2

6.7Degrees and radians#

Example 6.25

Degrees to radians

Type 180 and press D→R (MTH page 5, third key).
180◀MTHAPPSNXTNXTNXTNXTF3

Example 6.26

Radians to degrees

Type 3.14159265359 and press R→D (fourth key).
3.14159265359◀MTHAPPSNXTNXTNXTNXTF4

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