Both cos(π) and cos(-π) equal to 1 because cosine is an even function. By definition, an even function satisfies the condition that f(-x) = f(x) for all x. In the case of cosine, this means:
- cos(π) = -1
- cos(-π) = -1
However, cos(0) = 1, which might be confusing here. To clarify:
- When you evaluate cos(π), you are looking at the angle π radians, which lies on the negative x-axis on the unit circle. The coordinates at this point are (-1, 0), so cos(π) = -1.
- For cos(-π), you are evaluating the angle -π radians, which is also located on the negative x-axis. Thus, cos(-π) = -1 as well.
Therefore, cos(π) and cos(-π) are both equal to -1, not 1. It seems there was an error in the initial assumption that they equal 1. To sum up, both cos(π) and cos(-π) equal to -1 because cosine is an even function and both angles point to the same location on the unit circle.