MATHS CALCULATOR

MATHEMATICAL FORMULAS

Basic Identities

Definitions:

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

Additive Identity

a + 0 = a

 

Additive Inverse

a + (-a) = 0

 

Associative of Addition

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

 

Commutative of Addition

a + b = b + a

 

Subtraction

a – b = a + (-b)

 

Multiplicative Identity

a * 1 = a

 

Multiplicative Inverse

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

 

Multiplication times 0

a * 0 = 0

 

Associative of Multiplication

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

 

Commutative of Multiplication

a * b = b * a

 

Distributive Law

a(b + c) = ab + ac

 

Definition of Division

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)

 

Radicals √

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
  • b: Length of Adjacent
  • 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

Trigonometric Transformations

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