Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation will give you an idea of what the experiment will look like. For more information, you can visit this simple harmonic motion website. You are given the equation , which models the position of the weight with respect to time. You need to find the amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the time(s) at which the weight is at a particular position. To find this information, you need to convert the equation to the first form, .

a. Use the information above and the trigonometric identities to prove that .