# Deriving an equation for theta via the Projectile Motion Trajectory Eq

• lightlightsup
In summary, the individual is seeking help with a math problem involving finding the value of theta in an equation with multiple variables. They mention knowing some trig identities and finding the answer on Wikipedia, but are still curious to see someone derive the solution. They also mention that theta is currently impossible for them to solve without guidance.
lightlightsup
Homework Statement
Given all the other variables in this equation, find theta.
Relevant Equations
Y = x(tanθ)-[(gx^2)/(2(v0cosθ)^2)]
Perhaps I should ask this question in the math section of these forums.
But, I'm stumped and I don't think this equation is solvable?
Find theta given all the other variables:

Do you know some trig identities relating tan, sec, cos and their squares?

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.

Last edited:
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 two that solve it are ##\frac 1\cos=sec## and ##\sec^2=1+\tan^2##. Those reduce it to a quadratic in tan.

lightlightsup

## 1. What is the Projectile Motion Trajectory Equation?

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.

## 2. How is theta related to the Projectile Motion Trajectory Equation?

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.

## 3. How can I derive an equation for theta using the Projectile Motion Trajectory Equation?

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.

## 4. What is the significance of theta in projectile motion?

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.

## 5. Can theta be calculated using the Projectile Motion Trajectory Equation?

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.

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