To find the angle [tex]\( s \)[/tex] in the interval [tex]\(\left[0, \frac{\pi}{2}\right]\)[/tex] that satisfies [tex]\(\cos(s) = 0.7948\)[/tex], follow these steps:
1. Understand the Problem:
Given the cosine value, you need to find the corresponding angle [tex]\( s \)[/tex]. Since the cosine function is involved, use the inverse cosine function, which is commonly denoted as [tex]\(\arccos\)[/tex] or [tex]\(\operatorname{acos}\)[/tex].
2. Apply the Inverse Cosine Function:
To find [tex]\( s \)[/tex], apply the arccos function to the cosine value:
[tex]\[
s = \arccos(0.7948)
\][/tex]
3. Obtain the Numerical Value:
Use a calculator to find the numerical value of [tex]\(\arccos(0.7948)\)[/tex]. The value of [tex]\( s \)[/tex] approximately is:
[tex]\[
s \approx 0.6521
\][/tex]
4. Round the Result:
Ensure that the result is rounded to four decimal places, which is already confirmed above.
Thus, the value of [tex]\( s \)[/tex] that satisfies the given equation and is within the interval [tex]\(\left[0, \frac{\pi}{2}\right]\)[/tex] is:
[tex]\[
s = 0.6521 \quad \text{radians}
\][/tex]
