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4 problems match “principal values”. Clear

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1. Sum of inverse cosine and sine ●○○○○ 10 ptsFind the value of $\cos^{-1}\left(\frac{1}{2}\right) + 2\sin^{-1}\left(\frac{1}{2}\right)$. Give your answer in degrees.
2. Arcsine of sine of 10 ●●○○○ 20 ptsEvaluate $\sin^{-1}(\sin 10)$, where $10$ is in radians. Round your answer to two decimal places.
3. Sum of inverse sines of sines ●●○○○ 20 ptsCompute $\sin^{-1} (\sin 3) + \sin^{-1} (\sin 4) + \sin^{-1} (\sin 5).$ All functions are in radians.
4. Principal value with real poles ●●●○○ 50 ptsFind the Cauchy principal value of $\int_{-\infty}^{\infty}\frac{x\,dx}{(x-1)^4-1}$, where the poles at $0$ and $2$ lie on the real axis. Round to two decimal places.