The two that solve it are ##\frac 1\cos=sec## and ##\sec^2=1+\tan^2##. Those reduce it to a quadratic in tan.lightlightsup said:I know some trig identities and can lookup others.
But, it looks like I found the answer on Wikipedia.
P.S. This wasn't really the homework question. I was just curious when I looked at and derived the same trajectory equation that was in my book. But, then I started wonder if it could give me the other parameters. v was easy to find, x was harder. theta is impossible at my level of intelligence/knowledge (at least without guidance).
Nonetheless, i'd be curious to see someone derive this.
The Projectile Motion Trajectory Equation is a mathematical equation used to describe the path of a projectile in a uniform gravitational field. It takes into account the initial velocity, angle of launch, and acceleration due to gravity.
Theta (θ) is the angle of launch in the Projectile Motion Trajectory Equation. It represents the angle at which the projectile is launched relative to the horizontal.
To derive an equation for theta, we can rearrange the Projectile Motion Trajectory Equation to solve for theta. This can be done by using algebraic techniques, such as isolating theta on one side of the equation and taking the inverse sine or cosine of both sides.
Theta plays a crucial role in projectile motion as it determines the initial angle at which the projectile is launched. Changing the value of theta will result in different trajectories and landing points for the projectile.
Yes, theta can be calculated using the Projectile Motion Trajectory Equation if the other variables (initial velocity, angle of launch, and acceleration due to gravity) are known. It can also be calculated by using the measured distance and height of the projectile's landing point.