Final answer:
The value of cos(7pi) is evaluated by recognizing that the cosine function has a period of 2pi. Since 7pi is an odd multiple of pi, and cosine repeats every 2pi, cos(7pi) is equal to cos(pi), which is -1.
Step-by-step explanation:
To evaluate the trigonometric function cos(7pi) using its period as an aid, we first recognize that the cosine function is periodic with a period of 2pi. This means that the function repeats its values every 2pi radians. Specifically, cos(theta) = cos(theta + 2pi*n) for any integer n. In the case of cos(7pi), we can express 7pi as 6pi + pi, which is 3 times the period of the cosine function (2pi) plus pi.
Since 6pi is a multiple of the period, we can ignore it for evaluating the function. We are left with cos(pi), which yields -1 because cos(pi) equals -1. Therefore, cos(7pi) is also -1, as the additional periods do not change the value of the cosine function.