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

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

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

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

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

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

π6\frac{\pi}{6}

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

0≤θ≤π0 \leq \theta \leq \pi

Which identity relates inverse sine and inverse cosine?

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

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

π4\frac{\pi}{4}

Why must we restrict the domain of sine to have an inverse?

Only 1-to-1 functions have inverses

At which point does the graph of y=arcsin⁡xy = \arcsin x start?

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

What does sin⁡(arcsin⁡x)\sin(\arcsin x) equal?

xx

What is the domain of the inverse secant function sec⁡−1x\sec^{-1} x?

x≤−1x \leq -1 or x≥1x \geq 1

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