Final answer:
The cosine function has a maximum value of +1 and a minimum value of -1, which occur at angles of 0 degrees and 180 degrees, respectively.
"the correct option is approximately option A"
Step-by-step explanation:
The maximum and minimum values of the cosine function are crucial in trigonometry and relate to the function's amplitude on a coordinate system. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.
This value ranges as the angle changes from 0 degrees to 360 degrees or from 0 to 2π radians. The cosine function oscillates between its maximum value of +1 and its minimum value of -1. Therefore, when the angle is zero degrees, cosine reaches its maximum since cos(0) = 1, representing the instance where the length of the adjacent side and the hypotenuse are identical, with no parallel component.
As the angle increases past zero, the parallel component of the triangle's side adjacent to the angle increases while the hypotenuse remains constant, leading to a decrease in the cosine value. This decrease continues until an angle of 180 degrees or π radians, where the cosine function equals -1, representing its minimum value. Thus, the correct answer to the question is a) Maximum value is 1, minimum value is -1.