Final answer:
To find the vertical trace of the function cos(2x) cos(3y) at x = π/6, substitute x in the function with π/6 to obtain g(y) = (1/2)cos(3y), which is a cosine wave with amplitude of 1/2 along y-axis.
Step-by-step explanation:
The question refers to the vertical trace of a function, specifically the function f(x, y) = cos(2x) cos(3y), at a particular value of x, which is π/6. A vertical trace in this context means the intersection of the graph of the function with the plane that corresponds to the given x value, effectively plotting y versus f(x, y) while keeping x constant.
To find the vertical trace, we replace x in the function with π/6 and get a new function g(y) that depends solely on y:
g(y) = cos(π/3) cos(3y) which simplifies to g(y) = (1/2) cos(3y). This represents a cosine wave with an amplitude of 1/2 and period 2π/3 along the y-axis.
The vertical trace of the function at x = π/6 is a cosine function of y, with reduced amplitude, indicating how the function changes with respect to y while x is fixed.