# Available Functions

From WeBWorK

## 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: 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

Note that sometimes one or more of these functions is disabled for a WeBWorK problem because the instructor wants you to calculate the answer by some means other than just using the function.

- 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( ) or sin^-1() Another name for arcsin
- arccos( )
- acos( ) or cos^-1() Another name for arccos
- arctan( )
- atan( ) or tan^-1() Another name for arctan
- arccot( )
- acot( ) or cot^-1() Another name for arccot
- arcsec( )
- asec( ) or sec^-1() Another name for arcsec
- arccsc( )
- acsc( ) or csc^-1() Another name for arccsc
- sinh( )
- cosh( )
- tanh( )
- sech( )
- csch( )
- coth( )
- arcsinh( )
- asinh( ) or sinh^-1() Another name for arcsinh
- arccosh( )
- acosh( ) or cosh^-1()Another name for arccosh
- arctanh( )
- atanh( ) or tanh^-1()Another name for arctanh
- arcsech( )
- asech( ) or sech^-1()Another name for arcsech
- arccsch( )
- acsch( ) or csch^-1() Another name for arccsch
- arccoth( )
- acoth( ) or coth^-1() Another name for arccoth
- sqrt( )
- n! (n factorial -- defined for \(n\ge 0\)
- These functions may not always be available for every problem.
- sgn( ) The sign function, either -1, 0, or 1
- step( ) The step function (0 if \(x < 0\), 1 if \(x \geq 0\))
- fact(n) The factorial function n! (defined only for nonnegative integers)
- P(n,k) = n*(n-1)*(n-2)...(n-k+1) the number of ordered sequences of k elements chosen from n elements
- C(n,k) = "n choose k" the number of unordered sequences of k elements chosen from n elements