Difference between revisions of "Available Functions"
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Revision as of 18:26, 28 October 2009
Contents
Mathematical Symbols Available In WeBWorK
 + Addition
  Subtraction
 * Multiplication can also be indicated by a space or juxtaposition, 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: ()  You can also use square brackets, [ ], and braces, { }, for grouping, e.g. [1+2]/[3(4+5)]
Syntax for entering expressions
 Be careful entering expressions just as you would be careful entering expressions in 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 ('s and )'s to make your meaning clear. You can also use ['s and ]'s and {'s and }'s.
 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 enough to accept sin t or even sint. However, sin 2t is interpreted as sin(2)t, i.e. (sin(2))*t. Be careful.
 Do not enter sin^2t even though you might see something like this written in a text book. Mathematically speaking sin^2t is shorthand for (sin(t))^2(the square of sin of t) and must be entered this way. (You can enter it as sin(t)^2 or even sint^2, but don't try such things unless you really understand the precedence of operations. The "sin" operation has highest precedence, so it is performed first, using the next token (i.e. t) as an argument. Then the result is squared.)
 For example 2+3sin^2(4x) is wrong and will give an error message. You need to enter something like: 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 taken [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].
 Is 5^2 positive or negative? It's negative. This is because the square operation is done before the negative sign is applied. Use (5)^2 if you want to square negative 5.
 When in doubt use parentheses!!! :)
 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: 12+3 = (12)+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".
Mathematical Constants Available In WeBWorK
 pi This gives 3.14159265358979, e.g. cos(pi) is 1
 e This gives 2.71828182845905, e.g. ln(e*2) is 1 + ln(2)
Scientific Notation Available In WeBWorK
 2.1E2 gives 210
 2.1E2 gives .021
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
 cot( ) Note: cot( ) uses radian measure
 csc( ) Note: csc( ) uses radian measure
 exp( ) The same function as e^x
 log( ) This is usually the natural log but your professor may have redined this as log to the base 10
 ln( ) 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
 arccot( )
 acot( ) Another name for arccot
 arcsec( )
 asec( ) Another name for arcsec
 arccsc( )
 acsc( ) Another name for arccsc
 sinh( )
 cosh( )
 tanh( )
 sech( )
 csch( )
 coth( )
 arcsinh( )
 asinh( ) Another name for arcsinh
 arccosh( )
 acosh( ) Another name for arccosh
 arctanh( )
 atanh( ) Another name for arctanh
 arcsech( )
 asech( ) Another name for arcsech
 arccsch( )
 acsch( ) Another name for arccsch
 arccoth( )
 acoth( ) Another name for arccoth
 sqrt( )
 sgn( ) The sign function, either 1, 0, or 1
 step( ) The step function (0 if x < 0, 1 if x \geq 0)
 fact( ) The factorial function (defined only for nonnegative integers)