Question

Using the following trigonometic identity to neaton up your answer: 2cos(O)sin(O)=sin(2O). Look up what value of x( in degrees) makes sin(x) have it's largest value. Explain what angle (O) gives the longest range of a projectile with a given initial speed. Hint: What must (O) be in the expression sin(2O) for the function sin(x) to be a maximum.

Answer 1

O=\[\theta\]

Answer 2

The value of x that makes a sine function maximum is \[x=(4n+1) \pi/2\]. But since we are working with projectiles, we will take n=0
\[x=\pi/2\]
\[2O=\pi/2\]
\[O=\pi/4\]