Final answer:
The transition from 'cos x 12/12' to '5/13' is not a standard mathematical operation. The cosine function for an angle is defined as 'adjacent/hypotenuse' in a right triangle, and the correct cosine value requires specific triangle information. Without further context or proper setup, the change from '12/12' to '5/13' cannot be explained.
Step-by-step explanation:
It seems like there is a misunderstanding in the question regarding how cos x 12/12 could turn into 5/13. This might be related to the evaluation of a trigonometric function for a specific angle. To clarify, if we are given cos x where x is an angle, and if cos x equals 12/12, this simplifies to 1 because 12/12 is a fraction equal to 1. Cosine values range from -1 to 1, and there is no angle for which cos(θ) = 5/13 would simplify in the same way we simplify 12/12 to 1. However, if we have a right triangle where the lengths of the sides are known, we can find the cosine of an angle using the definition: cos(θ) = adjacent/hypotenuse. For example, if the adjacent side is 5 units and the hypotenuse is 13 units, then cos(θ) would be 5/13.
If there is a specific angle or triangle problem the student is referring to, we would need additional context to provide an exact solution. Otherwise, the transition from cos x 12/12 to 5/13 is not mathematically standard without more information about the problem setup.
According to trigonometry principles, for a right triangle in Figure 2.18, if the magnitude A and direction are known, we can solve for the scalar components using cos A = Ax/A and sin A = Ay/A.