Reciprocal & Inverse Trigonometric Functions (AQA A-Level Mathematics): Flashcards

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Reciprocal Trig Functions - Definitions
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Define cscθ\csc \theta

cscθ=1sinθ\csc \theta = \frac{1}{\sin \theta}

Define secθ\sec \theta

secθ=1cosθ\sec \theta = \frac{1}{\cos \theta}

Define cotθ\cot \theta

cotθ=1tanθ\cot \theta = \frac{1}{\tan \theta}

When is cscθ\csc \theta undefined?

When sinθ=0\sin \theta = 0

When is secθ\sec \theta undefined?

When cosθ=0\cos \theta = 0

Range of cscθ\csc \theta

(,1][1,)(-\infty, -1] \cup [1, \infty)

Range of secθ\sec \theta

(,1][1,)(-\infty, -1] \cup [1, \infty)

Pythagorean identity for csc\csc and cot\cot

csc2θ=1+cot2θ\csc^2 \theta = 1 + \cot^2 \theta

Pythagorean identity for sec\sec and tan\tan

sec2θ=1+tan2θ\sec^2 \theta = 1 + \tan^2 \theta

Simplify cscθsinθ\csc \theta \cdot \sin \theta

11

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