Reciprocal Trig Functions - Definitions (Edexcel A-Level Mathematics): Flashcards

Cosecant is $1/\sin\theta$, expressed as $\csc\theta = 1/\sin\theta$.

Undefined when $\sin \theta = 0$, at $\theta = n\pi$, $n$ integer.

Secant is $1/\cos(\theta)$, expressed as $\sec(\theta) = 1/\cos(\theta)$.

Undefined when $\cos \theta = 0$, at $\theta = (2n+1)\pi/2$.

Cotangent is $\cos \theta/\sin \theta$, or $\cot \theta = 1/\tan \theta$.

Undefined when $\tan \theta = 0$, at $\theta = n\pi$, $n$ integer.

Range is $(-\infty, -1] \cup [1, \infty)$.

Range is $(-\infty, -1] \cup [1, \infty)$.

The range of cotangent is all real numbers $(-∞, ∞)$.

$\csc^2 \theta = 1 + \cot^2 \theta$, derived from $\sin^2 \theta + \cos^2 \theta = 1$.