To solve for the given inverse trigonometric functions and round the results to the nearest degree, let's proceed step-by-step.
1. Calculate [tex]\( \sin^{-1}\left( \frac{2}{3} \right) \)[/tex]:
- First, input [tex]\( \frac{2}{3} \)[/tex] into the arcsine function on the calculator.
- The result will be in radians. Convert this result to degrees.
- Finally, round the result to the nearest degree.
By performing these steps, we find:
[tex]\[
\sin^{-1}\left( \frac{2}{3} \right) \approx 42^{\circ}
\][/tex]
2. Calculate [tex]\( \tan^{-1}(4) \)[/tex]:
- First, input [tex]\( 4 \)[/tex] into the arctangent function on the calculator.
- The result will be in radians. Convert this result to degrees.
- Finally, round the result to the nearest degree.
By performing these steps, we find:
[tex]\[
\tan^{-1}(4) \approx 76^{\circ}
\][/tex]
3. Calculate [tex]\( \cos^{-1}(0.1) \)[/tex]:
- First, input [tex]\( 0.1 \)[/tex] into the arccosine function on the calculator.
- The result will be in radians. Convert this result to degrees.
- Finally, round the result to the nearest degree.
By performing these steps, we find:
[tex]\[
\cos^{-1}(0.1) \approx 84^{\circ}
\][/tex]
So, in summary, the rounded values of the inverse trigonometric functions are:
[tex]\[
\begin{array}{l}
\sin^{-1}\left( \frac{2}{3} \right) = 42^{\circ} \\
\tan^{-1}(4) = 76^{\circ} \\
\cos^{-1}(0.1) = 84^{\circ}
\end{array}
\][/tex]
