39. Find the distribution of R = A sin , where A is a fixed constant and...

39. 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 = (v²/g) sin 2α, where g is the gravitational constant, equal to 980 centimeters per second squared.

THEORETICAL EXERCISES