Final answer:
The question seems to mix concepts from physics with the mathematical task of linearization. In mathematics, approximating arccos(0.9) would require additional information such as a nearby point and the derivative of arccos at that point. Without this, we cannot provide an accurate approximation using linearization.
Step-by-step explanation:
To approximate the cosine inverse (also known as arccos) of 0.9 using linearization, we can start with the fact that when the intensity is reduced by 90.0%, it remains 10.0% (or 0.100 times) its original value.
This concept is related to physics, particularly in optics where intensity and angles of incidence are related through the cosine squared relationship.
However, approximating the cosine inverse for 0.9 using linearization in mathematics would typically involve knowing the value of arccos at a nearby point and using the derivative of the arccos function to estimate the value.
Since we do not have a specific nearby point or its derivative given here, we cannot perform a mathematical linearization without additional information.