Suggestion: Print out this page and keep the hard copy handy while doing WeBWorK.

#### Mathematical Symbols Available In WeBWorK

• - Subtraction
• * Multiplication can also be indicated by a space or jutaposition, e.g., 2x, 2 x or 2*x, also 2(3+4).
• / Division
• ^ or ** You can use either ^ or ** for exponentiation, e.g., 3^2 or 3**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 are 3*4 and 3 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 want 2/(4+5) (which is 2/9).
• Don't enter 2/3*4 (which is 8/3) when you really want 2/(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 of sint or sin t. But WeBWorK is smart enought to accept sin t or even sint. But sin 2t is really sin(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. Use arcsin(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))^2 and it must be entered in the later way in WebWork. Note: sin(t)^2 is also acceptable. For example, 2+3sin^2(4x) is wrong. You need to enter it as: 2+3[sin(4x)]^2 or 2+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 value
• cos( ) Note: cos( ) uses radian measure
• sin( ) Note: sin( ) uses radian measure
• tan( ) Note: tan( ) uses radian measure
• sec( ) Note: sec( ) uses radian measure
• exp( ) The same function as e^x
• log( ) The natural log. NOTE!!
• ln( ) Another name for the natural log
• logten( ) The log to the base 10
• arcsin( )
• asin( ) Another name for arcsin
• arccos( )
• acos( ) Another name for arccos
• arctan( )
• atan( ) Another name for arctan
• sinh( ) Hyperbolic sine
• cosh( ) Hyperbolic cosine
• tanh( ) Hyperbolic tangent
• sech( ) Hyperbolic secant
• sqrt( ) Square root
• sgn( ) The sign function, either -1, 0, or 1
• step( ) 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

• 2.1E2 gives 210
• 2.1E-2 gives .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

Hobart and William Smith Colleges: Department of Mathematics and Computer Science