Mathematical Notation in WeBWorK

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Mathematical Symbols Available In WeBWorK

  • +
  • -
  • * Multiplication can also be indicated by a space or juxtaposition, e.g. 2x, 2 x or 2*x, also 2(3+4).
  • /
  • ^ or ** You can use either ^ or ** for exponentiation, e.g. 3^2 or 3**2
  • (
  • )

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 multiplication 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. But sin 2t is really sin(2)t, i.e. (sin(2))*t. Be careful.
  • Understand that sin^2t is really short hand for (sin(t))^2 and must be entered this way. Actually you could enter it as sin(t)^2 or even sint^2, but don't try such things unless you really understand the precedence of operations.
  • For example 2+3sin^2(4x) is wrong. 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].
  • 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".

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
  • 2.1E-2 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
  • exp( ) The same function as e^x
  • log( ) The natural log
  • 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( )
  • cosh( )
  • tanh( )
  • sech( )
  • sqrt( )