Inverse Trig Functions (AQA A-Level Mathematics): Flashcards

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Inverse Trig Functions
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Domain of sin⁡−1x\sin^{-1} x

−1≤x≤1-1 \leq x \leq 1

Range of sin⁡−1x\sin^{-1} x

−π2≤θ≤π2-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}

Domain of cos⁡−1x\cos^{-1} x

−1≤x≤1-1 \leq x \leq 1

Range of cos⁡−1x\cos^{-1} x

0≤θ≤π0 \leq \theta \leq \pi

Domain of tan⁡−1x\tan^{-1} x

−∞<x<∞-\infty < x < \infty (all real numbers)

Range of tan⁡−1x\tan^{-1} x

−π2<θ<π2-\frac{\pi}{2} < \theta < \frac{\pi}{2}

Identity: arcsin⁡x+arccos⁡x=\arcsin x + \arccos x =

π2\frac{\pi}{2}

Value of sin⁡−1(12)\sin^{-1}\left(\frac{1}{2}\right)

π6\frac{\pi}{6} (or 30°30°)

Value of arctan⁡(1)\arctan(1)

π4\frac{\pi}{4} (or 45°45°)

sin⁡(arcsin⁡x)=\sin(\arcsin x) =

xx (for xx in domain of arcsin⁡\arcsin)

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