Final answer:
The value for a that satisfies sin(a) = cos(25) is found using the co-function identity, resulting in a being 65 degrees, or 90 degrees minus the given angle 25 degrees.
Step-by-step explanation:
To find the value for a that makes sin(a) = cos(25) true, we can use the co-function identity which states that sin(90° - x) = cos(x). So, in order for sin(a) to be equal to cos(25), a must be equal to 90° - 25°, which simplifies to 65°.
The relationship between sine and cosine for complementary angles is key here. Complementary angles are two angles that add up to 90 degrees. Therefore, since 25 is the given angle, we subtract it from 90 degrees to get the complementary angle, which is the value for a.