To solve for the value of [tex]\(\cos^{-1}(0.7190)\)[/tex], we need to find the angle in radians whose cosine is 0.7190.
1. Identify the given value: We are given that the cosine of an angle is 0.7190.
2. Use the inverse cosine function: To find the angle itself, we would use the inverse cosine function, denoted as [tex]\(\cos^{-1}\)[/tex]. This function will give us the angle whose cosine is 0.7190.
3. Compute the angle: When we compute [tex]\(\cos^{-1}(0.7190)\)[/tex], we obtain an angle value.
4. Round the result: This computed angle should be rounded to three decimal places.
Following these steps, we find that:
[tex]\[ \cos^{-1}(0.7190) \approx 0.768 \text{ radians} \][/tex]
So, the approximate value of [tex]\(\cos^{-1}(0.7190)\)[/tex], rounded to three decimal places, is [tex]\(0.768\)[/tex] radians.
