Answer :
To find the values of the given inverse trigonometric functions and round them to the nearest degree, follow these steps:
### Step 1: Calculate [tex]\(\sin^{-1}\left(\frac{2}{3}\right)\)[/tex]
1. Input [tex]\(\frac{2}{3}\)[/tex] into the inverse sine function (often `asin` or `sin^-1`) on your calculator.
2. Convert the result from radians to degrees if necessary.
3. Round the result to the nearest degree.
After the calculation, the value of [tex]\(\sin^{-1}\left(\frac{2}{3}\right)\)[/tex] is approximately 42°.
### Step 2: Calculate [tex]\(\tan^{-1}(4)\)[/tex]
1. Input 4 into the inverse tangent function (often `atan` or `tan^-1`) on your calculator.
2. Convert the result from radians to degrees if necessary.
3. Round the result to the nearest degree.
After the calculation, the value of [tex]\(\tan^{-1}(4)\)[/tex] is approximately 76°.
### Step 3: Calculate [tex]\(\cos^{-1}(0.1)\)[/tex]
1. Input 0.1 into the inverse cosine function (often `acos` or `cos^-1`) on your calculator.
2. Convert the result from radians to degrees if necessary.
3. Round the result to the nearest degree.
After the calculation, the value of [tex]\(\cos^{-1}(0.1)\)[/tex] is approximately 84°.
### Summary of Results:
[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]
These are the rounded values of the given inverse trigonometric functions.
### Step 1: Calculate [tex]\(\sin^{-1}\left(\frac{2}{3}\right)\)[/tex]
1. Input [tex]\(\frac{2}{3}\)[/tex] into the inverse sine function (often `asin` or `sin^-1`) on your calculator.
2. Convert the result from radians to degrees if necessary.
3. Round the result to the nearest degree.
After the calculation, the value of [tex]\(\sin^{-1}\left(\frac{2}{3}\right)\)[/tex] is approximately 42°.
### Step 2: Calculate [tex]\(\tan^{-1}(4)\)[/tex]
1. Input 4 into the inverse tangent function (often `atan` or `tan^-1`) on your calculator.
2. Convert the result from radians to degrees if necessary.
3. Round the result to the nearest degree.
After the calculation, the value of [tex]\(\tan^{-1}(4)\)[/tex] is approximately 76°.
### Step 3: Calculate [tex]\(\cos^{-1}(0.1)\)[/tex]
1. Input 0.1 into the inverse cosine function (often `acos` or `cos^-1`) on your calculator.
2. Convert the result from radians to degrees if necessary.
3. Round the result to the nearest degree.
After the calculation, the value of [tex]\(\cos^{-1}(0.1)\)[/tex] is approximately 84°.
### Summary of Results:
[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]
These are the rounded values of the given inverse trigonometric functions.
