To find the angle [tex]\(\theta\)[/tex] when given [tex]\(\cos \theta = 0.9218\)[/tex], we need to follow these steps:
1. First, determine the angle in radians using the arccosine function, since [tex]\(\theta = \cos^{-1}(0.9218)\)[/tex].
2. Next, convert the angle from radians to degrees. The conversion formula from radians to degrees is:
[tex]\[
\theta (\text{degrees}) = \theta (\text{radians}) \times \frac{180}{\pi}
\][/tex]
3. Finally, round the resulting angle to the nearest tenth of a degree.
Let's go through the steps:
1. Using the arccosine function, the angle in radians is approximately:
[tex]\[
\theta (\text{radians}) \approx 0.3981
\][/tex]
2. Converting this angle from radians to degrees:
[tex]\[
\theta (\text{degrees}) \approx 0.3981 \times \frac{180}{\pi} \approx 22.8093
\][/tex]
3. Rounding this value to the nearest tenth of a degree gives us:
[tex]\[
\theta \approx 22.8^{\circ}
\][/tex]
Therefore, the angle [tex]\(\theta\)[/tex] is approximately [tex]\(22.8^{\circ}\)[/tex].
