An object is attached by a string to the end of a spring. When the weight is released it starts oscillating vertically in a periodic way that can be modeled by a trigonometric function.

Question

The object's average height is −20 cm (measured from the top of the spring). It achieves that average height every 2 seconds, and its maximum and minimum heights are each 5 cm from its average height.
Find the formula of the trigonometric function that models the height H of the weight t seconds after it reached its maximum height. Define the function using radians.

The answer says, "We know the object reaches its highest point at t=0, so let's use a cosine function."

How do I determine the maximum value is at t=0? This problem doesn't mention at what time the maximum value of the function occurs, only that it is 5 cm from the average height. Since the problem doesn't state where the max occurs, periodic behavior could be modeled by either a sine or cosine function.

Answer 1

The problem states:

Find the formula of the trigonometric function that models the height H of the weight t seconds after it reached its maximum height.

Your function is supposed to model the height starting when it is at its maximum. So, let that be t=0.