Let's solve for the values of the inverse trigonometric functions step-by-step and round each to the nearest degree:
### Step 1: Calculate [tex]\( \sin^{-1}\left(\frac{2}{3}\right) \)[/tex]
To find the inverse sine of [tex]\(\frac{2}{3}\)[/tex], we use the inverse sine function (also known as arcsine).
The result is approximately:
[tex]\[ \sin^{-1}\left(\frac{2}{3}\right) \approx 41.81^\circ \][/tex]
Rounded to the nearest degree:
[tex]\[ \sin^{-1}\left(\frac{2}{3}\right) \approx 42^\circ \][/tex]
### Step 2: Calculate [tex]\( \tan^{-1}(4) \)[/tex]
To find the inverse tangent of 4, we use the inverse tangent function (also known as arctangent).
The result is approximately:
[tex]\[ \tan^{-1}(4) \approx 75.96^\circ \][/tex]
Rounded to the nearest degree:
[tex]\[ \tan^{-1}(4) \approx 76^\circ \][/tex]
### Step 3: Calculate [tex]\( \cos^{-1}(0.1) \)[/tex]
To find the inverse cosine of 0.1, we use the inverse cosine function (also known as arccosine).
The result is approximately:
[tex]\[ \cos^{-1}(0.1) \approx 84.26^\circ \][/tex]
Rounded to the nearest degree:
[tex]\[ \cos^{-1}(0.1) \approx 84^\circ \][/tex]
### Final Results
Summarizing, the values of the inverse trigonometric functions rounded to the nearest degree are:
[tex]\[
\begin{array}{l}
\sin^{-1}\left(\frac{2}{3}\right) \approx 42^\circ \\
\tan^{-1}(4) \approx 76^\circ \\
\cos^{-1}(0.1) \approx 84^\circ \\
\end{array}
\][/tex]
