# Basic Trigonometric Formulae

## Trigonometric transformation formulas

Trigonometric Transformation Formulas: The set of formulas which are useful in transforming sums and difference of trigonometric functions into their products and vice versa. These sets of formulas are derived directly from Trigonometric Addition and Subtraction formulas. Here we will derive the transformation formulas using following four formulas which are Trigonometric addition and subtraction formulas: If we add and subtract the first two and last two equations in the equations above then we can get the following equations:   Now...

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## Trigonometric multiple and sub-multiple angle formulas

Trigonometric multiple and sub-multiple angle formulas: Prerequisite: Please consider studying following topics before you study this article for better grasp and understanding: Trigonometric addition and subtraction formulas Trigonometric Functions Pythagorian Identities   In this tutorial we shall derive formula for trigonometric functions of multiple and sub-multiple angle  , For example:   etc. Trigonometric multiple angle formulas: Under the trigonometric multiple angle formulas we shall derive the formulas for double and triple...

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## Trigonometric Addition and Subtraction formulae

Trigonometric Addition ( Sum ) and Subtraction ( Difference ) formula: The formulae which are popularly known as addition ( sum ) and subtraction( difference ) formulae are as follows: Sine of sum of angles:   Cosine of sum of angles:   Sine of difference of angles:   Cosine of difference of angles:   And similarly the sum and difference of angle formula of Tangent are: and,     Proof of Trigonometric Sum and Difference Formulae:   Now let us prove the identities or formulae listed above. In the...

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## Distance Formula

Basic Distance Formula: The basic distance formula states that: The distance “d” between two points A(x1,y1) and B(x2,y2) can be calculated as:   Using this Distance Formula of coordinate geometry we can establish fundamental trigonometric formulae for general angles in a very elegant way. So we shall now prove or derive this formula:   Derivation or Proof of Distance Formula: In the adjoining figure , “d” is the distance between two points P(x1 , y1) and Q(x2 , y2). Now let us draw “PL”...