Final answer:
To find the value of k, we need to determine where the line l is tangent to the graph of y=cos(x). We can find the value of k by setting the derivative of y=cos(x) equal to the line's slope, which is 0. Therefore, k can be A. π/2, B. π, C. 3π/2, or D. 2π.
Step-by-step explanation:
To find the value of k, we need to determine where the line l is tangent to the graph of y = cos(x). Since the line is tangent at the point (k, cos(k)), we can find the value of k by setting the derivative of y = cos(x) equal to the line's slope.
The derivative of y = cos(x) is -sin(x). The slope of the tangent line is equal to the derivative. So, we set -sin(k) equal to the slope of the line, and solve for k. Since the slope of a line tangent to the graph of y = cos(x) is always 0, we have -sin(k) = 0. This implies that k = nπ, where n is an integer. Therefore, the value of k can be either A. π/2, B. π, C. 3π/2, or D. 2π.