# Mathematical Notation in WeBWorK

## 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( )