# Identities & Reciprocals

## What is an identity?

An identity is when two terms are "the same as" each other, over the normal equals meaning "is equal to". For example $$x=6$$ is not an identity, but $$2x=x+x$$ is. An identity is represented by an equals-sign-like symbol with three horizontal lines: $$\equiv$$. You can write them with a regular $$=$$, as this is obviously still true.

## Trig identities you need to know

The two identities which you need to learn for trigonometry are:

$\frac{\sin(\theta)}{\cos(\theta)}\equiv\tan(\theta)$
$\sin^2(\theta)+\cos^2(\theta)\equiv1$

Where $$\theta$$ is any angle

## Reciprocal functions

The reciprocal functions of Sine, Cosine and Tangent are Cosecant (Cosec or Csc), Secant (Sec) and Cotangent (Cot) repectively. \begin{align} \frac{1}{\sin(\theta)}& \equiv\csc(\theta) \\[8pt] \frac{1}{\cos(\theta)}& \equiv\sec(\theta) \\[8pt] \frac{1}{\tan(\theta)}& \equiv\cot(\theta)\equiv\frac{\cos(\theta)}{\sin(\theta)} \end{align}

#### A way of remembering which is which

If we look at the abbrivations Cosec, Sec and Cot; the third letter of each is the same as the first of its reciprocal: