Deriving an equation for theta via the Projectile Motion Trajectory Eq

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Homework Help Overview

The discussion revolves around deriving an equation for the angle theta in the context of projectile motion, specifically using the trajectory equation. The original poster expresses uncertainty about the solvability of the equation for theta when other variables are known.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of trigonometric identities related to tangent and secant, with some questioning the feasibility of deriving theta from the given parameters. The original poster reflects on their own understanding and expresses a desire for guidance in the derivation process.

Discussion Status

Some participants have offered insights into trigonometric identities that may assist in the derivation. The conversation appears to be ongoing, with multiple interpretations and approaches being explored without reaching a consensus.

Contextual Notes

The original poster notes that the problem was not part of their homework but rather a curiosity stemming from their study of the trajectory equation. They mention varying levels of confidence in their mathematical abilities, particularly regarding the derivation of theta.

lightlightsup
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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:
Trajectory Eq.png
 
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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)
2c5c375af9d89e403690dceeb6d074eab6ed27fe

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. o0)
2c5c375af9d89e403690dceeb6d074eab6ed27fe

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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