Solve

Highest Position Needle Lowest Position Needle B } 9 a Note: Figure not drawn to scale 3. A sewing machine rapidly lowers and raises a threaded needle through a small slot in a steel plate. One full cycle consists of the needle moving from its highest position to its lowest position and then returning back to its highest position. The needle completes 12 full cycles every second. Point B is at the bottom tip of the needle. As the needle moves up and down, the height of point B above the steel plate periodically increases and decreases. At time =0 seconds, B is located at its highest position, 9 millimeters directly above the steel plate. At its lowest position, B is 5 millimeters directly below the steel plate. The sinusoidal function 4 models the height of B above the steel plate, in millimeters, as a function of time f, in seconds. A positive value of h(t) indicates B is above the steel plate; a negative value of h(t) indicates B is below the steel plate. (A) The graph of h and its dashed midline for two full cycles is shown. Five points, F', G, J, K, and P are labeled on the graph. No scale is indicated, and no axes are presented. Determine possible coordinates (t, h(t)) for the five points F, G, J, K, and P. Fo P (B) The function / can be written in the form h (t) =acos ( ( + c)) +d. Find values of the constants a,b,c, andd