Question: is 45 degrees the best angle of trajectory?
Answer: The sine function reaches its largest output value, 1, with an input angle of 90 degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. ... That means that the best way to launch a high-altitude projectile is to send it flying at a 90-degree angle to the ground—straight up.