Unit 19 More Functions

Function names and their abbreviations are considered math operations. They are transcribed in Nemeth Code, and their abbreviated letters are considered one math symbol.

Sine, Cosine, Tangent

Sine, cosine, and tangent (sin, cos, tan) are functions used in trigonometry to measure angles of a right triangle. In Nemeth Code, sine, cosine, and tangent are transcribed in their abbreviated form (sin, cos, tan).

Exception: An unabbreviated function name used in literary context, unconnected to a math expression, can be transcribed in UEB (Example: Today we will learn about tangent).

Sine, sin	⠎⠊⠝
Cosine, cos	⠉⠕⠎
Tangent, tan	⠞⠁⠝

Note: Examples that are not embedded in UEB have omitted the Nemeth Code switch indicators.

Example:

tan 61° = 1.804

⠞⠁⠝⠀⠼⠖⠂⠘⠨⠡⠀⠨⠅⠀⠼⠂⠨⠦⠴⠲

No space precedes these function names, but a space is required after the function name regardless of the print spacing.

Examples:

sin 30° cos 45°

⠎⠊⠝⠀⠼⠒⠴⠘⠨⠡⠉⠕⠎⠀⠼⠲⠢⠘⠨⠡

$y = 3\cos 2x$

⠽⠀⠨⠅⠀⠼⠒⠉⠕⠎⠀⠼⠆⠭

sin(𝛼 + 𝛽) + sin(𝛼 − 𝛽)

⠎⠊⠝⠀⠷⠨⠁⠬⠨⠃⠾⠬⠎⠊⠝⠀⠷⠨⠁⠤⠨⠃⠾

An English letter indicator (ELI) is not used with a single letter or short form letter combination that follows a function name, it is considered part of the expression.

Examples:

sin x

⠎⠊⠝⠀⠭

sin C

⠎⠊⠝⠀⠠⠉

Examples of functions written between Nemeth Code switch indicators:

Find the value of cos(60°).

⠠⠋⠔⠙⠀⠮⠀⠧⠁⠇⠥⠑⠀⠷⠀⠸⠩⠀⠉⠕⠎⠀⠷⠖⠴⠘⠨⠡⠐⠾⠀⠸⠱⠲

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

⠠⠉⠁⠇⠉⠥⠇⠁⠞⠑⠀⠸⠩⠀⠹⠎⠊⠝⠀⠨⠹⠌⠉⠕⠎⠀⠨⠹⠼⠀⠸⠱

Other spacing rules take precedence over the spacing rules for functions such as Nemeth Code switch indicators, or signs of comparison.

Examples:

$\theta\, = \, 30{^\circ}\,\therefore\,\sin\theta\, = \,\frac{1}{2}$

⠨⠹⠀⠨⠅⠀⠼⠒⠴⠘⠨⠡⠀⠠⠡⠀⠎⠊⠝⠀⠨⠹⠀⠨⠅⠀⠹⠂⠌⠆⠼

* Note: The spacing for symbols of comparison take precedence over the "no space before a function" rule.

$\frac{1}{cos}$

⠹⠂⠌⠉⠕⠎⠼

* Note: There is no space between "cos" and the closing fraction indicator.

And More Functions

Logarithm, log	⠇⠕⠛
Factorial ! (product of integers)	⠯
Absolute Value \|x\|	⠳⠭⠳

A logarithm is the inverse function of an exponent. An exponent uses a superscript number called a power or exponent. A log uses a subscript number called a base.

For example, a number 2, raised to the power of 4, gets you 16.

2⁴= 16

⠼⠆⠘⠲⠀⠨⠅⠀⠼⠂⠖

A logarithm with a base of 2, to get you 16, is multiplied 4 times.

Log₂ 16 = 4

⠇⠕⠛⠆⠀⠼⠂⠖⠀⠨⠅⠀⠼⠲

* Remember that the subscript indicator is not used when a baseline character is a letter or abbreviated function name and the subscript is numeric.

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.

4! = 1*2*3*4 = 24

⠼⠲⠯⠀⠨⠅⠀⠼⠂⠈⠼⠼⠆⠈⠼⠼⠒⠈⠼⠼⠲⠀⠨⠅⠀⠼⠆⠲

6! = 720

⠼⠖⠯⠀⠨⠅⠀⠼⠶⠆⠴

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. Absolute value shows the magnitude of a number.

Examples:

|27|

⠳⠆⠶⠳

|-3| = 3

⠳⠤⠒⠳⠀⠨⠅⠀⠼⠒

|x| = |- x|

⠸⠩⠀⠳⠭⠳⠀⠨⠅⠀⠳⠤⠭⠳⠀⠸⠱

Is it true that: -|-5| = -(5) = -5?

⠠⠊⠎⠀⠭⠀⠞⠗⠥⠑⠀⠞⠒⠀⠸⠩⠀⠤⠳⠤⠢⠳⠀⠨⠅⠀⠤⠷⠢⠾⠀⠨⠅⠀⠤⠼⠢⠀⠸⠱⠦

Brain Boost

Common Constants and Concepts

Pi π	⠨⠏
Euler's Number 𝑒	⠈⠑
Imaginary Number 𝒾	⠊
Infinity ∞	⠠⠿

A mathematical constant is a fixed value for a mathematical definition used in expressions, equations and formulas. The following are some common constants and the concept for infinity.

Pi

The ration between the circumference and the diameter of a circle.

π = 3.14159265 …

⠨⠏⠀⠨⠅⠀⠼⠒⠨⠂⠲⠂⠢⠔⠆⠖⠢⠀⠄⠄⠄

Euler's Number

Also known as the exponential growth constant.

𝑒 = 2.7182 …

⠈⠑⠀⠨⠅⠀⠼⠆⠨⠶⠂⠦⠆⠀⠄⠄⠄

Imaginary Number

It is called an imaginary number because in reality there is no such thing as a negative square root.

$i\, = \sqrt{- 1}$

⠊⠀⠨⠅⠀⠜⠤⠂⠻

Infinity

Infinity is the concept of endlessness. It is often used as if it is a real number, but it does not behave as a real number.

∞+∞ = ∞

⠠⠿⠬⠠⠿⠀⠨⠅⠀⠠⠿

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