# 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.

2^{4 }= 16

⠼⠆⠘⠲⠀⠨⠅⠀⠼⠂⠖

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

Log_{2} 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

⠳⠤⠒⠳⠀⠨⠅⠀⠼⠒

$\left|x\right|=\left|-x\right|$⠸⠩⠀⠳⠭⠳⠀⠨⠅⠀⠳⠤⠭⠳⠀⠸⠱

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.

∞+∞ = ∞

⠠⠿⠬⠠⠿⠀⠨⠅⠀⠠⠿