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

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Inverse Trig Functions
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What is the range of sin⁡−1x\sin^{-1} x?

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

What is the domain of tan⁡−1x\tan^{-1} x?

All real numbers

What is the range of cos⁡−1x\cos^{-1} x?

0≤θ≤π0 \leq \theta \leq \pi

What is the value of sin⁡−1(12)\sin^{-1}\left(\frac{1}{2}\right)?

π6\frac{\pi}{6}

What is the value of arctan⁡(1)\arctan(1)?

π4\frac{\pi}{4}

What identity relates arcsin⁡x\arcsin x and arccos⁡x\arccos x?

arcsin⁡x+arccos⁡x=π2\arcsin x + \arccos x = \frac{\pi}{2}

Where does the graph of y=arcsin⁡xy = \arcsin x start and end?

(−1,−π2)(-1, -\frac{\pi}{2}) to (1,π2)(1, \frac{\pi}{2})

What domain restriction makes y=sin⁡xy = \sin x one-to-one?

−π2≤x≤π2-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}

What are the horizontal asymptotes of y=arctan⁡xy = \arctan x?

y=−π2y = -\frac{\pi}{2} and y=π2y = \frac{\pi}{2}

What is the value of cos⁡−1(−32)\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)?

5π6\frac{5\pi}{6}

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