Special Values¶
Some math answers require entering constants, special numbers, or non-numeric values. This page covers how to enter them.
Boxes that take only a number
Constants such as pi and exact forms such as sqrt(2)/2 work only in answer boxes that accept a calculation. If the box's hint says to enter an integer or decimal number, type a decimal: pi, sqrt(2)/2 and even 1/2 are marked wrong there. DNE and oo are accepted in both kinds of box.
Mathematical Constants¶
| Value | How to enter | Notes |
|---|---|---|
| π (pi) | pi |
Lowercase only; Pi and PI are not recognized and are marked wrong |
| 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 letter o's) |
| Negative infinity (−∞) | -oo |
inf and infinity are not recognized and are marked wrong. Typing or pasting the ∞ symbol also works.
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 |
| No solution | Select the No solution option if the question shows one; otherwise enter DNE, unless the question asks you to type something else |
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 (∅) | Usually DNE. If the box asks for a set in braces, such as {-4, 3, 2}, enter {}. Interval answers written as inequalities also accept empty set, but the live check flags it as invalid; DNE works without a warning |
Used when the solution set of an equation is empty, e.g., "no real solutions."
Boolean / Logical Values¶
Most true/false questions are multiple choice: select the option. If a question asks you to type the answer, type the word it asks for. Typed answers are compared as text, so T is not accepted when the expected answer is true (capitalization usually does not matter).
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 ∞.