Powers, roots, logs and trig

4.1Powers and square roots#

Type a power with ^: the cursor moves up into the exponent, and ▶ brings it back down. x² squares the previous value. ctrl√x² builds a square root; press ▶ to leave the root.

Example 4.1

A big power stays exact

$$2^{64}=18446744073709551616$$

1. Type 2, power, 64, enter.

   2^64enter

Example 4.2

Square root simplified

$$\sqrt{12}=2\sqrt{3}$$

1. Press ctrl then the square key, type 12, then right and enter.

   ctrl√x²12▶enter

Example 4.3

Cube root

$$\sqrt[3]{27}=3$$

1. Press ctrl then the power key, type 3, right, then 27 and enter.

   ctrlⁿ√^3▶27enter

Example 4.4

Fractional exponent

$$27^{2/3}=9$$

1. Type 27, power, (2/3) and enter.

   27^(2÷3)enter

4.2Logarithms and e to a power#

ln is the natural log (base $e$) and log is base 10. With ctrl they become the inverse functions $e^x$ and $10^x$. For any other base use the log template in the templates menu, or type log(8,2).

Example 4.5

Natural log of e squared

$$\ln\left(e^{2}\right)=2$$

1. Type ln( e ^ 2 ) and enter.

   ln(e^2▶)enter

Example 4.6

Base 10 log

1. Type log(1000).

   log(1000)enter

Example 4.7

Ten to a power

1. Press ctrl log, type 3.

   ctrl10ˣlog3enter

Example 4.8

Log with another base

$$\log_{2}8=3$$

1. Open templates, choose log_(), type 2, right, 8.

   templates62▶8enter

Example 4.9

e squared and its decimal

1. Press ctrl ln, type 2, right, then ctrl enter.

   ctrleˣln2▶ctrl≈enter

4.3Sine, cosine and tangent#

Trig answers are exact when the angle is a familiar one. The Angle setting decides whether the angle is read in radians (default), degrees or gradians. The Trig menu also holds secant, cosecant, cotangent and the hyperbolic functions.

Example 4.10

Sine of pi over six

1. Type sin( π / 6 ).

   sin(π÷6)enter

Example 4.11

Sine of pi over four

1. Type sin( π / 4 ).

   sin(π÷4)enter

Example 4.12

Inverse sine

1. Press ctrl then sin, type 1/2, close the bracket.

   ctrlsin⁻¹sin1÷2)enter

Example 4.13

Use a degree sign

$$\sin 30^\circ=\frac{1}{2}$$

1. Type sin( 30, ctrl dot (degree sign) ).

   sin(30ctrl°.)enter

Example 4.14

Secant from the Trig menu

$$\sec\frac{\pi}{3}=2$$

1. Press trig, choose 7 (sec), type π/3 and close.

   trig7π÷3)enter

Example 4.15

Hyperbolic cosine

1. Press trig, choose B (cosh), type 0.

   trigb0)enter

4.4The constants π, e and i#

Example 4.16

Pi as a decimal

1. Press pi, then ctrl enter.

   πctrl≈enter

Example 4.17

Euler number as a decimal

1. Press e, then ctrl enter.

   ectrl≈enter

Example 4.18

Euler identity

$$e^{i\pi}=-1$$

1. Type e ^ ( ctrl-i × π ).

   e^(ctrl𝑖ππ)enter

4.5Number functions: gcd, lcm, mod, rounding#

The Number menu (menu, 2) holds these functions. Each one is a name followed by a bracket; type the arguments separated by ,.

Example 4.19

Greatest common divisor

1. Type gcd(12,18).

   gcd(12,18)enter

Example 4.20

Least common multiple

1. Type lcm(4,6).

   lcm(4,6)enter

Example 4.21

Remainder

1. Type mod(17,5).

   mod(17,5)enter

Example 4.22

Is it prime?

1. Type isprime(97).

   isprime(97)enter

Example 4.23

Factor a number into primes

$$360=2^3\cdot 3^2\cdot 5$$

1. Type factor(360).

   factor(360)enter

Example 4.24

Round to two places

1. Type round(π,3).

   round(π,3)enter

Example 4.25

Floor of a negative decimal

1. Type floor(−2.5).

   floor((−)2.5)enter

4.6Factorials, permutations and combinations#

Example 4.26

Factorial

$$5!=120$$

1. Type 5, then ctrl then x (the ! key).

   5ctrl!xenter

Example 4.27

Combinations

$$\binom{5}{2}=10$$

1. Type nCr(5,2).

   ncr(5,2)enter

Example 4.28

Permutations

1. Type nPr(5,2).

   npr(5,2)enter

rand() gives a random decimal between 0 and 1, and randInt(a,b) gives a random whole number between a and b. They give a different answer every time.