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.
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