Throwing events in track and field include the shot put, the discus throw, the hammer throw, and the javelin throw. The distance that the athlete can achieve depends on the initial speed of the object thrown and the angle above the horizontal at which the object leaves the hand. This angle is represented by x in the figure shown. The distance, d, in feet, that the athlete throws is modeled by the formula in which v is the initial speed of the object thrown, in feet per second, and x is the angle, in degrees, at which the object leaves the hand. a. Use an identity to express the formula so that it contains the sine function only.
b. Use your formula from part a to find the angle that produces the maximum distance, d, for a given initial speed, v.