# A calculus of the absurd

##### 7.3.3 Secant, cosecant, cotangent and friends

These are a pain to remember. All of these functions are defined as the reciprocal of a trig function (I remember someone saying that they’re not exactly defined like this because, mumble, mumble division by zero, mumble, mumble), but the basic idea is this:

• Definition 7.3.1 We define

\begin{align} & \csc (\theta ) = \frac {1}{\sin (\theta )} \\ & \sec (\theta ) = \frac {1}{\cos (\theta )} \\ & \cot (\theta ) = \frac {1}{\tan (\theta )} \end{align}

Here’s a helpful trick for remembering this

• 1. cosecant $$\mapsto$$ $$\sin$$

• 2. secant $$\mapsto$$ $$\cos$$

• 3. cotangent $$\mapsto$$ $$\tan$$