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Deriving an equation for theta via the Projectile Motion Trajectory Eq

Homework Statement
Given all the other variables in this equation, find theta.
Homework 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:
Trajectory Eq.png
 

haruspex

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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. o0)

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:

haruspex

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Homework Helper
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I know some trig identities and can lookup others.
But, it looks like I found the answer on Wikipedia. o0)

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.
 

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