Final answer:
The question involves converting rectangular coordinates to polar coordinates using the relationships between x and y components and r and θ in a function z(x,y).
Step-by-step explanation:
The student's question involves the concept of converting rectangular coordinates to polar coordinates, particularly focusing on the relationships between the x and y components and the polar coordinates represented by r and θ (theta). The question provides the definition of a function z(x,y) = xy, where x = rcos(5θ). To find the corresponding y value in terms of polar coordinates, we use the relation y = r × sin that converts from polar to rectangular coordinates.
The provided examples and strategic descriptions allude to the use of cosine in various contexts, like vector analysis and trigonometry in physics problems. It demonstrates that cosine and sine functions are used to find components of vectors and to solve for magnitudes and directions in different scenarios.