Task of the Week: Sine Gate and Cosine

A special task on the subject of trigonometric functions will be presented this week within our category “Task of the Week”.

Task: Sine Gate and Cosine (Task Number: 4554)

The cemetery is accessible through a curved gate. The upper end can be approximated by a cosine function ƒ(x) = a⋅cos(b⋅x). Give the product of a and b as the result (x and y axis in cm).

First, the gate must be tranferred to a suitable coordinate system. In order to be able to solve the problem, it must then be clarified which influcences a and b have on the function and how they can be determined. a is the amplitude and is half the difference between the maximum and minimum y-values. The gate is exactly one period long. The stretching factor is thus calculated by the width of the gate along the x-axis with b = 2π ÷ (width of the gate). In this case, the solution is validated using the product of a and b. Alternatively, it would also be possible to use multiple choice.