A parametric equation is a set of equations that express the coordinates of a point in terms of one or more parameters. These parameters can be variables, constants, or functions that define the position of the point.
To find the parametric equation of a function, you need to determine the values of the parameters that correspond to the coordinates of the points on the graph of the function. In this case, the parameters would be x and y, and the corresponding coordinates would be the values of the function at those points.
The maximum value of the function y = cos x is 1, which occurs when x = 0. This is because the cosine function oscillates between -1 and 1, and at x = 0, it reaches its highest value of 1.
To find the coordinates of the maximum point of a function, you need to set the derivative of the function equal to zero and solve for the variable. In this case, the maximum point occurs when the derivative of y = cos x is equal to 0, which is at x = π/2. Substituting this value into the original function gives us the coordinates (π/2, 1).
The parametric equation for y = cos x with max at (3, 5) is x = π/2 + 3 and y = 5. This means that the x-coordinate of any point on the graph will be the value of π/2 plus 3, and the y-coordinate will always be 5. This equation satisfies both the condition of the maximum point and the shape of the cosine function.