Sure! Let's find the values of the inverse trigonometric functions and round them to the nearest degree. Here are the steps to solve each part:
1. Calculate [tex]\(\sin^{-1}\left(\frac{2}{3}\right)\)[/tex]:
- Use a scientific calculator to find the inverse sine (also called arcsine) of [tex]\(\frac{2}{3}\)[/tex].
- Input [tex]\(\frac{2}{3}\)[/tex] and then use the [tex]\(\sin^{-1}\)[/tex] function to get the result in degrees.
- Once you have the result, round it to the nearest degree.
[tex]\[
\sin^{-1}\left(\frac{2}{3}\right) \approx 42^\circ
\][/tex]
2. Calculate [tex]\(\tan^{-1}(4)\)[/tex]:
- Use a scientific calculator to find the inverse tangent (also called arctangent) of 4.
- Input 4 and then use the [tex]\(\tan^{-1}\)[/tex] function to get the result in degrees.
- Once you have the result, round it to the nearest degree.
[tex]\[
\tan^{-1}(4) \approx 76^\circ
\][/tex]
3. Calculate [tex]\(\cos^{-1}(0.1)\)[/tex]:
- Use a scientific calculator to find the inverse cosine (also called arccosine) of 0.1.
- Input 0.1 and then use the [tex]\(\cos^{-1}\)[/tex] function to get the result in degrees.
- Once you have the result, round it to the nearest degree.
[tex]\[
\cos^{-1}(0.1) \approx 84^\circ
\][/tex]
So, the results are:
[tex]\[
\sin^{-1}\left(\frac{2}{3}\right) \approx 42^\circ
\][/tex]
[tex]\[
\tan^{-1}(4) \approx 76^\circ
\][/tex]
[tex]\[
\cos^{-1}(0.1) \approx 84^\circ
\][/tex]
These are the rounded values to the nearest degree for the given inverse trigonometric functions.
