Functions

Sine, Cosine, Tangent

Sine, cosine, and tangent (sin, cos, tan) are trigonometric ratios of right triangles. They are transcribed in their abbreviated form (sin, cos, tan). They may appear contracted unless they are already in uncontracted mode.

sine, sin	⠎⠔
cosine, cos	⠉⠕⠎
tangent, tan	⠞⠁⠝

A function name is written unspaced from its related number.

Examples:

tan 61^{°} = 1.804

⠞⠁⠝⠼⠋⠁⠘⠚⠀⠐⠶⠀⠼⠁⠲⠓⠚⠙

$\sin 39$

⠎⠔⠼⠉⠊

A function name directly preceding or following a letter requires a space to separate it from the function name unless it is separated by a parenthesis or other braille indicator.

Examples:

$\sin x + 2$

⠎⠔⠀⠭⠐⠖⠼⠃

$x\cos{}$

⠰⠭⠀⠉⠕⠎

$3\sin x$

⠼⠉⠎⠊⠝⠀⠰⠭

Note: The function sin is not contracted after the numeric indicator.

The following three examples separate the function from the letter with a grouping symbol or indicator, so no space is needed.

Examples:

Separated by parenthesis

$\sin(x + 2)$

⠎⠔⠐⠣⠭⠐⠖⠼⠃⠜

Separated by a capital letter indicator

$\sin X$

⠎⠔⠠⠭

Separated by a Greek letter indicator

$\frac{1}{\cos\theta}$

⠰⠷⠼⠁⠨⠌⠉⠕⠎⠨⠹⠾

Separated by a fraction indicator

$\sin\frac{\pi}{15}$

⠎⠔⠰⠷⠨⠏⠨⠌⠼⠁⠑⠾

More Examples:

$\alpha = b\frac{\sin\alpha}{\sin\beta}$

⠨⠁⠀⠐⠶⠀⠃⠰⠷⠎⠔⠨⠁⠨⠌⠎⠔⠨⠃⠰⠾

$\tan\theta = \ \frac{\sin\theta}{\cos\theta}$

⠞⠁⠝⠨⠹⠀⠐⠶⠀⠰⠷⠎⠔⠨⠹⠨⠌⠉⠕⠎⠨⠹⠰⠾

$\lim_{\theta\ \rightarrow 0}{\cos\theta}$

⠰⠰⠇⠊⠍⠨⠢⠣⠨⠹⠳⠕⠼⠚⠜⠉⠕⠎⠨⠹

Logarithmic Functions (log)

A logarithm is the inverse function of an exponent. An exponent uses a superscript "power", a log uses a subscript number called a base. Level change indicators rules are followed to show the base of a logarithm.

Like other functions, the log function name is written unspaced from its related number.

Logarithm, log

⠇⠕⠛

Like sin, cos, and tan, the function name log is written unspaced from its related number, but spaced from its related letter unless it is separated by a parenthesis or other braille indicator.

Examples:

$\log_{2}(50)$

⠇⠕⠛⠰⠢⠼⠃⠐⠣⠼⠑⠚⠐⠜

$\log_{7}36$

⠇⠕⠛⠰⠢⠼⠛⠼⠉⠋

$\log x$

⠇⠕⠛⠀⠰⠭

${5\log}_{x}$

⠼⠑⠇⠕⠛⠢⠭

$x\ \log$

⠰⠭⠀⠇⠕⠛

$\log_{e}$

⠇⠕⠛⠰⠢⠑

$\log_{e}16 = \ln 16$

⠇⠕⠛⠰⠢⠑⠼⠁⠋⠀⠐⠶⠀⠇⠝⠼⠁⠋

Note: Lowercase LN (ln) is considered natural log and follows the same rules as the log function.

Factorial

A factorial is the product of a number and all the numbers that come before it. A factorial symbol is unspaced from its related term.

Factorial ! (product of integers)

⠖

Examples:

$3! = 1*2*3 = 6$

⠼⠉⠖⠀⠐⠶⠀⠼⠁⠐⠔⠼⠃⠐⠔⠼⠉⠀⠐⠶⠀⠼⠋

$n! = n(n - 1)$

⠰⠝⠖⠀⠐⠶⠀⠝⠐⠣⠝⠐⠤⠼⠁⠐⠜

Absolute Value

Vertical bars are used to show absolute value, or how far a number is from zero on a number line either to the left or to the right. The vertical bar symbols are placed before and after the number or term.

Vertical bar |

⠸⠳

Examples:

$|25|$

⠸⠳⠼⠃⠑⠸⠳

$|x| = | - x|$

⠸⠳⠭⠸⠳⠀⠐⠶⠀⠸⠳⠐⠤⠭⠸⠳

$|\overrightarrow{xy}|$

⠰⠰⠸⠳⠣⠭⠽⠜⠘⠱⠸⠳

$\sqrt{x^{2}}\ = \ |x|$

⠰⠩⠭⠰⠔⠼⠃⠬⠀⠐⠶⠀⠸⠳⠭⠸⠳

Differentiation and Derivatives

Calculous differentiation and derivatives are written using all previously learned mathematical letters, symbols, and rules for grouping, level changes, functions, fractions, radicals, Greek letters, modifiers, prime and double prime. Pay attention to when grade 1 indicators are needed.

Examples:

$d(y)$

⠙⠐⠣⠽⠐⠜

$d\lbrack f(x)\rbrack$

⠙⠨⠣⠋⠐⠣⠭⠐⠜⠨⠜

$\frac{dy}{dx}$

⠰⠷⠙⠽⠨⠌⠙⠭⠰⠾

$fʺ(x) = 3x - 4$

⠰⠰⠋⠶⠶⠐⠣⠭⠐⠜⠀⠐⠶⠀⠼⠉⠭⠐⠤⠼⠙

Integration

Integration requires one additional symbol, and the grade 1 indicator is required unless the mode is already in uncontracted mode. The integral sign is unspaced from its function and treats its limits as subscript and superscripts.

Integral sign ∫

⠮

Examples:

$\int_{}^{}{2(x)dx}$

⠰⠮⠼⠃⠐⠣⠭⠐⠜⠙⠭

$\int_{a}^{b}{f(x)dx}$

⠰⠰⠮⠢⠁⠔⠃⠋⠐⠣⠭⠐⠜⠙⠭

Previous - Next