The decimal approximation for $\cos(90^\circ - 3.99^\circ)$ is approximately 0.0695824, rounded to seven decimal places.

Do you need any further details or have any questions?
Here are some related questions to explore:

1. What is the sine of $90^\circ - 3.99^\circ$?
2. How does the identity $\cos(90^\circ - \theta) = \sin(\theta)$ apply here?
3. What is the cosine of 3.99 degrees directly?
4. How would the value change for a different angle, say 10 degrees?
5. What is the relationship between sine and cosine for complementary angles?

Tip: The co-function identity, $\cos(90^\circ - \theta) = \sin(\theta)$, can simplify many trigonometric calculations.