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:


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:

Remeber trig inverses