Special Values¶
Some math answers require entering constants, special numbers, or non-numeric values. This page covers how to enter them.
Mathematical Constants¶
| Value | How to enter | Notes |
|---|---|---|
| π (pi) | pi |
Case-insensitive; Pi and PI also work |
| e (Euler's number) | e |
The base of the natural logarithm |
| i (imaginary unit) | i |
Used in complex number questions |
Examples:
- Area of unit circle:
pi - e to the power of 2:
e^2 - Complex number:
3+2i
Infinity¶
| Value | How to enter |
|---|---|
| Positive infinity (∞) | oo (two lowercase letter o's) or inf or infinity |
| Negative infinity (−∞) | -oo or -inf or -infinity |
Examples:
- Limit as x → ∞:
oo - Interval from −∞ to 5:
(-oo, 5]
Does Not Exist / Undefined¶
| Value | How to enter |
|---|---|
| Does not exist | DNE |
| Undefined | DNE or undefined |
| No solution | none or no solution (check the specific question) |
Use DNE when a limit does not exist, a function is undefined at a point, or a value cannot be determined.
Empty Set¶
| Value | How to enter |
|---|---|
| Empty set (∅) | {} or emptyset |
Used when the solution set of an equation is empty, e.g., "no real solutions."
Boolean / Logical Values¶
Some questions ask for true/false answers. Enter:
trueorTfalseorF
Special Angles and Exact Trig Values¶
When a question asks for an exact value of a trigonometric expression, enter the exact form rather than a decimal approximation:
| Expression | Exact answer |
|---|---|
| sin(π/6) | 1/2 |
| cos(π/4) | sqrt(2)/2 |
| tan(π/3) | sqrt(3) |
Checking the Preview¶
After entering a special value, check the preview below the input box to confirm the system recognized it correctly. For example, pi should preview as the π symbol, and oo should preview as ∞.