** **

** **

__The Multiple
Trigonometric Calculator__

__Performs Over 45
Simultaneous Calculations__

__© 2010 by____ __**David-Alyy@TechForText.com**

__A new type of online trigonometry calculator is presented
on this website. This calculator is also provided in the Excel and
OpenOffice.org formats, for download. The calculators are provided for
free and they are not trials with a time limit. __

** **

The website that provides the free
OpenOffice.org software package is located at **www.openoffice.org**.
**You
can access this site by left clicking on these words.**

If you want information about the __Multiple
Trigonometric Calculator, and related concepts, scroll down.__

__Description and
Instructions for the__

__Multiple Trigonometric Calculator__

__Basic Description of the
Calculator__

The Multiple Trigonometric Calculator is displayed online in one very wide webpage that has eight sections. This webpage can be scrolled from left to right, and from right to left, and it provides only a minimal of the top-down scrolling of conventional web pages.

The calculated results of the
Multiple Trigonometric Calculator are displayed on all eight sections of its
webpage. The results are displayed in categories, such as __length of
the three sides of the triangle__, __area__, __perimeter__, etc.

The Excel and OpenOffice versions of this calculator function and look similar to the online version, and they are also viewed by scrolling from left to right and right to left.

__Instructions__

** **

The Multiple Trigonometric Calculator is very easy to
use. It only has two input boxes, which are colored pink, and placed at
the beginning of the webpage, to make them easy to locate. To use the
Calculator, delete the numbers in the two pink boxes, and enter your own
numbers. ** These numbers are for the height and angle of a right
triangle,** which is illustrated at the beginning of the webpage.
After entering the numbers, left click with the mouse on the background.
For the online version, you can also left click on a calculation button, and
for the Excel and OpenOffice.org formats you can press the enter key.

After completing the above, the
Calculator will provide OVER 45 calculated results, which will be displayed
throughout the eight sections of the website, in ** red
numbers**. (If you do not have a solid background in
trigonometry, some of the calculated results might be unfamiliar to you.)

__Two Types of Calculation
Sequences __

__Carried Out by the
Multiple Trigonometric Calculator__

__And Other Dedicated
Mathematical Software__

** **

** **

** **

__Introduction__

The
following is background information. It is not necessary to master this
material to use the __Multiple Trigonometric Calculator.__ However, the
material consists of two concepts that relate to the way calculations are
performed, within the software, which I am calling __computation in series__,
and __computation in parallel__. These concepts are useful for
designing and building complex dedicated mathematical software, and they do not
just apply to the Multiple Trigonometric Calculator. However, the
Trigonometric Calculator is a useful example, to illustrate the concepts.

__Computation
in Series __

The Multiple Trigonometric Calculator performs some of the calculations
in a chain like sequence, one after another. This is done when the result
of one calculation is required to calculate the next calculation. This
involves a __series__ of two or **MORE** dependent calculations. In more
general terms it involves a series of steps that must be performed in a
predefined sequence, by the computer, such as step 1, step 2, step 3, step 4,
etc. The steps can be mathematical calculations, or any other set of
processes that can be performed by a computer. I am calling this concept __computation
in series. __

When the Multiple Trigonometric
Calculator calculates the perimeter of a right triangle, it involves ** computation
in series,** consisting of the following steps:

Step one) Calculates the cotangent, based on the value the user entered for angle A

Step two) Then, it calculates the length of the adjacent leg of the triangle, by multiplying the length of the opposite side by the cotangent. (The length of the opposite side is entered by the user.)

Step three) Based on the length of the adjacent leg,
calculated above, and the length of the opposite side, the length of the
hypotenuse of the triangle is calculated. This is done with the __Pythagorean
Theorem__. (Incidentally, the hypotenuse is also calculated in an
alternative way by the Calculator, using trigonometry.)

0

The yellow diagram at the end of this paragraph represents
__computation in __

** Series,** or a sequential set of calculations (steps or electronic
components), where the calculated result (or functionality) of the first
computation is needed for the second, the second needed to calculate the third,
etc. It is analogous to electronic components connected in a series.

The
green diagram below represents ** computation in parallel,** or
calculations, a set of steps, or electronic components, that are not dependent on
each other, and they can be calculated or function simultaneously and
independently of each other. This is analogous to electronic components
connected in parallel.

__The Similarity Between The
Principles Of Dataflow And Electron Flow In A Circuit, As Expressed Above, Is
Not A Coincidence__

It is perhaps not surprising that the same concepts, as expressed above, apply to electronic circuits and calculation devices. Keep in mind that calculation devices are essentially electronic, and they transmit and process data in terms of electronic pulses that ultimately travel through wires or other metal conductors, into electronic components.

The above discussion of series and parallel connections,
was greatly simplified. Most electronic circuits, and complex calculation
devices, contain extremely complex electronic or data flow patterns. This
often involves flow patterns that are parallel at one level, but they may also
have a set of components or formulas connected in series. In general,
series and parallel connections can converge and very complex ways. This level of complexity can be
seen by examining the complex dataflow patterns involve with the __Multiple
Trigonometric Calculator.__

__Critical Calculations__

The Multiple Trigonometric Calculator was primarily designed for general use, study, homework, and demonstration purposes. However, it was NOT designed for critical calculations, where a mathematical error can lead to the loss of life, injury, property damage, or the loss of large sums of money, such as with major engineering projects, and nuclear power plants. If the Multiple Trigonometric Calculator is used for such a purpose, each calculation must be checked by at least one or two other calculation devices. The other calculation devices should be run on different operating systems, such as Macintosh or Linux, and with computer processes made by different manufacturers, such as Intel and AMD. The data should be entered by different individuals. This is because, in rare cases, malfunctions in software and/or hardware can result in mathematical errors, but the biggest and most important risk factor is data entry errors.

__Calculation Devices and Critical
Calculations__

Calculation devices can be constructed for critical
calculations, to prevent data entry errors, and to detect malfunctions in
software or hardware, but I did not provide these features in the Multiple
Trigonometric Calculator. (If you need calculation devices with such
features, I can create them to meet your needs. You can contact me at ** David-Alyy@TechForText.com **or see the last section of this
webpage.)

__Calculation Devices Designed for
Critical Calculations__

However, even software designed with the special features mentioned above, or any other calculation device, should be checked with another software package, on a different operating system, with a different individual doing the data entry, for each and every highly critical calculation.

__Number Crunching Ability
of The__

__Multiple Trigonometric
Calculator__

The Multiple Trigonometric Calculator
in all three formats, online, Excel, and OpenOffice, may display very large or
very small numbers in scientific notation. The letter E is used to
designate scientific notation. The online version uses a lowercase __e__,
and the Excel and OpenOffice versions use an uppercase __E__. This
format is illustrated in the following examples.

__Examples of the Display of Very
Large Numbers__

__In Scientific Notation, Using the
Letter E.__

** **

1000000000000000000000 is displayed as 1e+21. The 21, with a plus sign, (+) represents the number of decimal places after the first digit. This can be clarified by counting the 21 red highlighted digits in the following: 1000000000000000000000

1456789666666890000000 is displayed as 1.45678966666689e+21. The 21 represents the number of decimal places after the first digit. This can be seen by counting the digits highlighted in red as follows: 1456789666666890000000

** **

__Examples of the Display of Very
Small Numbers__

__In Scientific Notation, Using the
Letter E.__

** **

0.000000000000000000001 is displayed as 1e-21. With this example, 21 with the minus sign represent the number of decimal places after the decimal point, as indicated by the 21 digits highlighted in red as follows: 0.000000000000000000001

The number 0.0000000000000000000067987 is displayed as 6.7987e-21. Note the 21 with the minus sign (-) represent the number of decimal places after the decimal point. This becomes clear by counting the digits highlighted in red as follows: 0.0000000000000000000067987

__Very large Numbers, and the__

__Multiple Trigonometric Calculator__

When very large numbers, such as 1e+306 are calculated,
you will usually get an error message, such as NaN,** **#NUM! or #VALUE!** **

__Very Small Numbers, and the__

__Multiple Trigonometric Calculator__

** **

When calculated results are infinitesimally small, (such
as 1e-350) the calculator will round the number down to **0** (zero).

__Entering Very Large and Very Small
Numbers, __

__Into the Pink Input Boxes,__

__Of the Multiple Trigonometric
Calculator__

The two pink input boxes of the Multiple Trigonometric Calculator can hold numbers with over 300 digits. However, if you enter more than 15 digits, you may not be able to see the entire number, but this will not affect the accuracy of calculated results. If you enter more than 21 digits the calculator will usually convert the number to scientific notation, which will make the entire number visible.

However, if you enter extremely
large and numbers, especially for exponents, the Calculator may provide an error
message as explained above. Sometimes, you will get results for only a portion
of the calculations available in the ** Multiple Trigonometric Calculator.**
Keep in mind, I am not talking about hundreds of trillions; I'm talking
about numbers much greater, such as 1e-200.

__This Website and the
Multiple Trigonometric Calculator was Designed and Built by__

__David-Alyy@TechForText.com
__

I design and build user-friendly software based
calculation devices for __arithmetic__, __accounting__, __currency
exchange rates__,
__algebra__, __trigonometry__, __correlations__,
__calculus__, etc. I also create attractive online calculation devices
for websites. For a list of my websites with calculation devices
see www.TechForText.com/Math

I generally make these devices in the Microsoft Excel, OpenOffice.org, and the JavaScript formats, but I can work with other spreadsheet formats besides the above.

I can create new types of web communication forms for your website, such as the form on the top of this page. This can also include forms with built-in calculation devices.

I write instructions for the devices I build. I can also write instructions for software and computer devices created by others. In addition, I can write advertising for your websites, products and services.

For a detailed list of all the services I offer, see www.TechForText.com For a list of all my websites see www.David100.com

I can provide the services mentioned above on a fee-for-service basis, or possibly based on temporary or permanent employment. If you are interested in my services, and want additional contact information or more data on the services I offer, you can email me at David-Alyy@TechForText.com or use the website communication form, on the top of this page. My resume is online at: www.David100.com/R

I am located in the USA. If you are a great distance from my locality or are in another country, this is not important. I can provide these services worldwide, because the software and websites I make can be delivered through the Internet to any locality, providing there are no governmental restrictions.