Problem

Use the ALEKS calculator to evaluate each expression. Give your answers in radians. Round them to the nearest hundredth. If applicable, click on "Undefined." \[ \begin{array}{c} \sin ^{-1}(1.17)=\square \\ \tan ^{-1}(0.46)=\square \\ \cos ^{-1}(-0.52)=\square \end{array} \]

Solution

Step 1 :\(\sin^{-1}(1.17)\): Since 1.17 is not in the domain of \(\sin^{-1}(x)\), this expression is undefined.

Step 2 :\(\tan^{-1}(0.46)\): This is within the domain of \(\tan^{-1}(x)\), so we can calculate it. Using a calculator, we find that \(\tan^{-1}(0.46) \approx 0.43\) radians (rounded to the nearest hundredth).

Step 3 :\(\cos^{-1}(-0.52)\): This is within the domain of \(\cos^{-1}(x)\), so we can calculate it. Using a calculator, we find that \(\cos^{-1}(-0.52) \approx 2.09\) radians (rounded to the nearest hundredth).

Step 4 :So, the solutions are:

Step 5 :\(\boxed{\sin^{-1}(1.17) = \text{Undefined}}\)

Step 6 :\(\boxed{\tan^{-1}(0.46) = 0.43 \text{ radians}}\)

Step 7 :\(\boxed{\cos^{-1}(-0.52) = 2.09 \text{ radians}}\)

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Source: https://solvelyapp.com/problems/BEk0Gebhb0/

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