Sure! Let's find the values of the inverse trigonometric functions using a calculator, and then round them to the nearest degree.
### 1. [tex]\(\sin^{-1} \left( \frac{2}{3} \right)\)[/tex]
To find [tex]\(\sin^{-1}(x)\)[/tex], also known as arcsin, we input [tex]\(\frac{2}{3}\)[/tex] into the calculator's inverse sine function and convert the result from radians to degrees if necessary. This yields a certain degree which is then rounded to the nearest whole number.
The value of [tex]\(\sin^{-1} \left( \frac{2}{3} \right)\)[/tex] rounded to the nearest degree is:
[tex]\[ \sin^{-1} \left( \frac{2}{3} \right) \approx 42^\circ \][/tex]
### 2. [tex]\(\tan^{-1}(4)\)[/tex]
To find [tex]\(\tan^{-1}(x)\)[/tex], also known as arctan, we input 4 into the calculator's inverse tangent function and convert the result from radians to degrees if necessary. This yields a certain degree which is then rounded to the nearest whole number.
The value of [tex]\(\tan^{-1}(4)\)[/tex] rounded to the nearest degree is:
[tex]\[ \tan^{-1}(4) \approx 76^\circ \][/tex]
### 3. [tex]\(\cos^{-1}(0.1)\)[/tex]
To find [tex]\(\cos^{-1}(x)\)[/tex], also known as arccos, we input 0.1 into the calculator's inverse cosine function and convert the result from radians to degrees if necessary. This yields a certain degree which is then rounded to the nearest whole number.
The value of [tex]\(\cos^{-1}(0.1)\)[/tex] rounded to the nearest degree is:
[tex]\[ \cos^{-1}(0.1) \approx 84^\circ \][/tex]
So, the rounded values of the inverse trigonometric functions 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]
These are the values rounded to the nearest degree.
