# MATHS CALCULATOR # MATHEMATICAL FORMULAS

## Basic Identities

### Definitions:

• a: Real Number a
• b: Real Number b
• c: Real Number c

a + 0 = a

a + (-a) = 0

(a + b) + c = a + (b + c)

a + b = b + a

a – b = a + (-b)

a * 1 = a

#### Multiplicative Inverse

a * (1/a) = 1 (if a is not 0)

a * 0 = 0

#### Associative of Multiplication

(a * b) * c = a * (b * c)

a * b = b * a

#### Distributive Law

a(b + c) = ab + ac

a / b = a(1/b)

## Exponents

### Definitions:

• a: Real Number a
• b: Real Number b
• x: Real Number x

x^a * x^b = x^(a + b)

x^a / x^b = x^(a – b)

a^x * b^x = (a*b)^x

a^x / b^x = (a/b)^x

(x^a)^b = x^(a*b) = (x^b)^a

## Logarithms

### Definitions:

• a: Real Number a
• b: Real Number b
• x: Real Number x

#### Definition of Logarithms

x = logb( a ) <=> b^x = a    (if a,b>0 and b ≠ 1)

#### Laws of Logarithms

log(a * b) = log(a) + log(b)

log( a^b ) = b * log(a)

log( a/b ) = log(a) – log(b)

### Definitions:

• a: Real Number a
• b: Real Number b
• n: Real Number x

## Compound Interest

### Definitions:

• r: Interest Rate in %
• n: Investment for n Years
• F: Value of Future Investment
• P: Value of Present Investment

## Percent Calculation

### Definitions:

• p: %
• S: Number
• R: Number
• x: Factor

What is p percent of value S?

R is p percent of what value S?

R is what percent p of value S?

What is the factor x for the percent of value p?

## Trigonometry ◿

### Definitions:

• a: Length of Opposite
• c: Length of Hypothenuse
• h: Length of Hypothenuse
• alpha: Angle α
• beta: Angle β
• gamma: Angle γ
• x: a/h
• y: b/h
• z: a/b
abcc²b²a²abcCABα

#### Pythagorean Theorem

In any right triangle, the area of the square whose side is the hypotenuse (c) is equal to the sum of the areas of the squares whose sides are the two legs (a, b).

acCABα

#### Sine

The sine function is a basic triogemetric function. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.

bcCABα

#### Cosine

The cosine function is a basic triogemetric function. In a right triangle, cosine gives the ratio of the length of the side adjacent to an angle to the length of the hypotenuse.

abCABα

#### Tangent

The tangent function is a basic triogemetric function. In a right triangle, tangent function gives the ratio of the length of the side opposite to an angle to the length of the adjacent.

abcCABαβγ