When launching a missile for a given range, the minimum velocity that is needed is related to the angle of the launch, and the velocity is determined by v = (2 cos 2Θ)/(2 + 2 cos 2Θ). Find the value of V when Θ = π/6

Question

When launching a missile for a given range, the minimum velocity that is needed is related to the angle of the launch, and the velocity is determined by v = (2 cos 2Θ)/(2 + 2 cos 2Θ).  Find the value of V when Θ = π/6

anonymous · Answer

$$v=\frac{ 2\cos (\frac{ 2\pi }{ 6 }) }{2 + 2\cos (\frac{ 2\pi }{ 6 })}$$
$$v=\frac{ 2\cos \frac{ \pi }{ 3} }{ 2 + 2\cos \frac{ \pi }{ 3 } }$$
$$v=\frac{ 2 \times \frac{ 1 }{ 2 } }{ 2 + 2 \times \frac{ 1 }{ 2 } }$$
$$v=\frac{ 1 }{ 2 + 1 }$$
$$v=\frac{ 1 }{ 3 }$$