## Mathematical Symbols Available In WeBWorK

+Addition-Subtraction*Multiplication can also be indicated by a space or jutaposition, e.g.,2x,2 xor2*x, also2(3+4)./Division^or**You can use either^or**for exponentiation, e.g.,3^2or3**2- Parentheses and brackets for grouping:
( ). You can also use square brackets,[ ], and braces, { }, for grouping, e.g.,[1+2]/[3(4+5)]- WeBWorK is case sensitive. Do NOT write "
X" when you really intend "x".

## Syntax for entering expressions

- Be careful entering mathematical expressions just as you would with a calculator.
- Sometimes using the
*symbol to indicate mutiplication makes things easier to read. For example(1+2)*(3+4)and(1+2)(3+4)are both valid. So are3*4and3 4(3 space 4, not 34) but using a * makes things clearer.- Use parentheses
( )to make your meaning clear. You can also use brackets[ ]and braces { }. For example

- Don't enter
2/4+5(which is 5.5) when you really want2/(4+5)(which is 2/9).- Don't enter
2/3*4(which is 8/3) when you really want2/(3*4)(which is 2/12).- Entering big quotients with square brackets, e.g.,
[1+2+3+4]/[5+6+7+8], is a good practice.- Be careful when entering functions. It's always good practice to use parentheses when entering functions. Write
sin(t)instead ofsintorsin t. But WeBWorK is smart enought to acceptsin tor evensint. Butsin 2tis reallysin(2)t, i.e.,(sin(2))*t. Be careful!- Do NOT use the notation
sin^-1(x),tan^-1(x), etc. for inverse trigonometric functions -- WeBWorK does not understand it. Usearcsin(x),arctan(x), etc., or the shorter forms of this:asin(x),atan(x), etc. See the list below of function notations understood by WeBWorK.- Powers of trigonometric functions. When we write sin^2t it is really shorthand for
(sin(t))^2and it must be entered in the later way in WebWork. Note:sin(t)^2is also acceptable. For example,2+3sin^2(4x)is wrong. You need to enter it as:2+3[sin(4x)]^2or2+3sin(4x)^2. Why does the last expression work? Because things in parentheses are always done first [i.e., (4x)], next all functions, such as sin, are evaluated [giving sin(4x)], next all exponents are evaluated [giving sin(4x)^2], next all multiplications and divisions are performed [giving 3sin(4x)^2], and finally all additions and subtractions are performed [giving 2+3sin(4x)^2].- The complete rules for the precedence of operations, in addition to the above, are

- Multiplications and divisions are performed left to right: 2/3*4 = (2/3)*4 = 8/3.
- Additions and subtractions are performed left to right: 1-2+3 = (1-2)+3 = 2.
- Exponents are taken right to left: 2^3^4 = 2^(3^4) = 2^81 = a big number.
- Use the "Preview Button" to see exactly how your entry looks. E.g. to tell the difference between 1+2/3+4 and [1+2]/[3+4] click the "Preview Button".
- NOTE: Many students who think WeBWorK is refusing a correct answer are actually making algebra mistakes, sometimes minor, sometimes serious. Please check your algebra and syntax before submitting your answer.
- Do not use exclamation points to denote factorials. WeBWorK does not understand things like 3! -- use fact(3) to denote 3 factorial.

## Mathematical Constants Available In WeBWorK

pi: This gives 3.14159265358979, e.g. cos(pi) is -1. (Note that this is a good estimate of the actual value of $\pi$.) Do NOT write Pi or PI.e: This gives 2.71828182845905, e.g. ln(e*2) is 1 + ln(2). (Note that this is a good estimate of the actual value of $e$.) Do NOT write E for e.

## Mathematical Functions Available In WeBWorK

abs( )The absolute valuecos( )Note: cos( ) uses radian measuresin( )Note: sin( ) uses radian measuretan( )Note: tan( ) uses radian measuresec( )Note: sec( ) uses radian measureexp( )The same function as e^xlog( )The natural log. NOTE!!ln( )Another name for the natural loglogten( )The log to the base 10arcsin( )asin( )Another name for arcsinarccos( )acos( )Another name for arccosarctan( )atan( )Another name for arctansinh( )Hyperbolic sinecosh( )Hyperbolic cosinetanh( )Hyperbolic tangentsech( )Hyperbolic secantsqrt( )Square rootsgn( )The sign function, either -1, 0, or 1step( )The step function (0 if x < 0, 1 if x >= 0)fact( )The factorial function (defined only for non-negative integers)

## Scientific Notation Available In WeBWorK

You will seldom need to use this, however

2.1E2gives 2102.1E-2gives .021

This material was adapted by Dr. Kevin Mitchell from http://webwork.uwyo.edu/webworkdocs/functions_and_symbols.html and can also be found on his web pages at http://math.hws.edu/~mitchell/WeBWorKSyntax.html