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=
θ

Answer 2

I'm assuming you can differentiate.
maximum value of any function occurs when the 1st derivative is 0, and the 2nd derivative is negative.
The derivative of sin is cos. That = 0 when angle = pi/2
any projectile will have a maximum range when the initial angle is pi/4.