SQR, for instance, is the familiar square root function, and
PRINT SQR 9
gives 3, the square root of 9. (To get SQR, you first press the FUNCTION key - shifted NEWLINE. This changes the cursor to
. Now press the SQR key (H): SQR appears on the screen and the cursor changes back to 
. The same method works for all the words that are written underneath the keys, almost all of which are function names.)Try
PRINT SQR 2
You can test the accuracy of the answer by
PRINT SQR 2*SQR 2
which ought to give 2. Note that both SQRs are worked out before the *, and in fact all functions (except one - NOT) are worked out before the five operations +, -, *, / and **. Again, you can circumvent this rule using brackets -
PRINT SQR (2*2)
gives 2.
Here are some functions (there is a complete list in appendix C). If your maths is not up to understanding some of these, it does not matter - you will still be able to use the computer.
SGN The sign function (sometimes called signum to avoid confusion with SIN). The result is -1, 0 or +1 according as the argument is negative, zero or positive.
ABS The absolute value, or modulus. The result is the argument made positive, so that
ABS -3.2 = ABS 3.2 = 3.2
SIN *
COS *
TAN *
ASN arcsin *
ACS arccos *
ATN arctan *
LN natural logarithm (to base 2.718281828459045..., alias e)
EXP exponential function
SQR square root
INT integer part. This always rounds down, so INT 3.9 = 3 & INT -3.9 = -4. (An integer is a whole number, possibly negative.)
PI
= 3.1415265358979..., the girth in cubits of a circle one cubit across. PI has no argument. (Only ten digits of this are actually stored in the computer, & only eight will be displayed.)RND Neither has RND an argument. It yields a random number between 0 (which value it can take) & 1 (which it cannot).
* The trigonometrical functions. These work in radians, not degrees.
Using the jargon of the last chapter, all these except PI & RND are unary operations with priority 11. (PI & RND are nullary operations, because they have no operands.)
The trigonometrical functions, & EXP, LN & SQR, are generally calculated to 8 digits accuracy.
RND & RAND: These are both on the same key, but whereas RND is a function, RAND is a keyword, like PRINT. RAND is used for controlling the randomness of RND.
RND is not truly random, but follows a fixed sequence of 65536 numbers that happen to be so jumbled up as to appear random (RND is pseudo-random). You can use RAND to start RND off at a definite place in this sequence by typing RAND, & then a number between 1 & 65535, & then NEWLINE. It's not so important to know where a given number starts RND off, as that the same number after RAND will always start RND off at the same place. For instance, type
RAND 1 & NEWLINE)
& then
PRINT RND
& type both these in turn several times. (Remember to use FUNCTION to get RND.) The answer from RND will always be 0.0022735596, not a very random sequence.
RAND 0
(or you can miss out the 0) acts slightly differently: it judges where to start RND off by how long the television has been on, & this should be genuinely random.
Note: In some dialects of BASIC you must always enclose the arguments of a function on brackets. This is not the case in ZX81 8K BASIC.
Summary
Statement: RAND
Functions: SGN. ABS, SIN, COS, TAN, ASN, ACS, ATN, LN, EXP, SQR, INT, PI, RND
FUNCTION
