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

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Reciprocal Trig Functions - Definitions
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Define csc⁡θ\csc \theta

csc⁡θ=1sin⁡θ\csc \theta = \frac{1}{\sin \theta}

Define sec⁡θ\sec \theta

sec⁡θ=1cos⁡θ\sec \theta = \frac{1}{\cos \theta}

Define cot⁡θ\cot \theta

cot⁡θ=1tan⁡θ\cot \theta = \frac{1}{\tan \theta}

When is csc⁡θ\csc \theta undefined?

When sin⁡θ=0\sin \theta = 0

When is sec⁡θ\sec \theta undefined?

When cos⁡θ=0\cos \theta = 0

Range of csc⁡θ\csc \theta

(−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty)

Range of sec⁡θ\sec \theta

(−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty)

Pythagorean identity for csc⁡\csc and cot⁡\cot

csc⁡2θ=1+cot⁡2θ\csc^2 \theta = 1 + \cot^2 \theta

Pythagorean identity for sec⁡\sec and tan⁡\tan

sec⁡2θ=1+tan⁡2θ\sec^2 \theta = 1 + \tan^2 \theta

Simplify csc⁡θ⋅sin⁡θ\csc \theta \cdot \sin \theta

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