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 \(\mapsto \) \(\tan \)