Final answer:
The question seems to contain a typo or missing information, making it unclear what value (a) represents. The values given for cosine and sine suggest they relate to angles in quadrant I, but without more context, we cannot determine a specific value for (a). Additional information or clarification is needed.
Step-by-step explanation:
The question is asking to find the value of (a), but since the question doesn't provide a clear context for what (a) represents, we'll assume there might be a typo or missing information. However, we can still discuss the trigonometric identities and the information provided. In particular, cosine and sine are both trigonometric functions that relate the angles of a triangle to the lengths of its sides in right-angled triangles, and they also define points on the unit circle for any angle.
Given that cos α = 0.094 and sin β = 0.913, and both of these angles are in quadrant I, we know their values are positive. The reference to quadrant I also tells us that the angles are between 0 and 90 degrees. However, without additional context or specific equations, we cannot directly calculate a value for (a). If (a) were representing an angle or a side in a triangle, we might use trigonometric identities such as those mentioned in the reference, like the Law of Sines or the Law of Cosines, but additional information would be required.
If you have more details or a specific formula you are working with, please provide that so we can give you a more accurate answer.