Find the distribution of r = a sin θ, where a is a fixed constant and θ is uniformly distributed on (−π/2, π/2). such a random variable r arises in the theory of ballistics. if a projectile is fired from the origin at an angle α from the earth with a speed v, then the point r at which it returns to the earth can be expressed as r = (v 2/g) sin(2α), where g is the gravitational constant, equal to 980 centimeters per second squared.