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First-Number Contants
In the Calcul-8-r program, you can make the first input number one of two mathematical constants: Pi (π) or the Natural Logarithm Base, e. Each of them are irrational numbers - they can't be absolutely expressed as fractions and as expressed as decimals, they go on forever and don't repeat any sequences of numbers. Pi approximately equals 3.1415926536, and e approximately equals 2.7182818285.
You can also do what I call answer recycling, that is use the answer you obtained as the first number of the next calculation. It is very useful for long chain math (e.g. you keep using the answer as the next number in the next calculation).
Basic Operations
The Four Basic Operations
These are the four operations you've known since first/second grade. They're the ones you've grown to love (or hate) and the one's that all other mathematics are based on. Nothing is simpler than adding, subtracting, multiplying, and dividing two numbers.
Exponential Operators
A little more advanced that the four basic functions, these are still very important. The x ^ y button raises x to the yth power. I even added the x ^ 2 button for squaring x (it is one of the most common forms of exponentation).
Modulo Operation
This operation returns the remainder after x is divided by y. For example, 20 mod 3 = 2, but 20 ÷ 3 = 6.666.
Trigonometric Functions
The following are trigonometric, or trig, functions. They are used to determine the measure of an angles in triangles. Trigonometry is used in a variety of careers; mainly in navigation, surveying, and engineering. In the following explinations, the Greek letter theta, θ, is used to stand for an unknown angle measure, but "X" is used in the Calcul-8-r program.
Sine - 
: Sine, for right triangles, is used to determine the measure of an angle and is equal to the opposite leg's length divided by the hypotenuse's length.
Cosine - 
: Cosine is also used to determine, in right triangles, the measure of an angle, but is equal to the adjacent leg's length divided by the hypotenuse.
Tangent - 
: Tangent is equal to 
.
Cotangent - 
: Cotangent is equal to 
.
Secant - 
: Secant is equal to 
.
Cosecant - 
: Cosecant is equal to 
.
Logarithm Functions
Base-10 Logarithm Function - 
The logarithm function determines the power of ten needed to achieve the value of the number. For example, if log(x) equals z, then 10z (10 to the zth power) equals x.
Logarithm of a Base - 
This function returns the logarithm of a base other than 10. If log2(x) equals z, then 2z equals x, for example.
Square Root - 
This function returns the square root of a number. A square root cancels out a square and vice versa.
Summation - 
The summation function returns the sum of all the number between 1 and the entered number. Σ(100) equals 1+2+3+4+5+...+97+98+99+100 which equals 5050. The formula to do this is (n(n+1)) ÷ 2.
Factorial - 
The factorial function is equal to the product of all the numbers from 1 to the entered number, so if the entered number was 10, then 10! equals 1x2x3x...x9x10, or 3,628,800.
Fahrenheit To/From Celsius - 
These two functions deal with temperature conversion. They allow you to convert between Fahrenheit and Celsius. Very useful if you aren't familiar with one or the other.
Specific Calculators
Clicking the Specific Calculators will bring up the Specific Calculators dialog box. It is populated by the Tax/Discount Calculator and the Interest Calculator; more will be added as I get some more ideas.
The Tax/Discount Calculator calculates the tax or discount when provided with a subtotal and a percentage rate. Input both of these figures, select the radio button corresponding to the desired option, and click Go. Your tax/discount amount will be displayed along with your total after the tax has been added or the discount has been deducted.
The Interest Calculator calculates the interest on any loan taken from, or any deposit given to, a bank. The principal is that loan/deposit, the rate is a percentage, and the time is how long (in years) the loan is taken out (or the deposit is planned to be depositted). If Compound Interest is selected, you will also be asked how often the principal is compounded.
LaTeX Equation Display
The box at the bottom, titled "Official Math Format", displays the calculation that was just performed as a LaTeX equation and the Clear buttom at the bottom of the box clears the image, but it the image refreshes automatically each time a new calculation is performed.