Eliminate Parametric to Derive x and y in tan(t)+sec(t) and tan(t)-sec(t)

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Homework Help Overview

The discussion revolves around the parametric equations x = tan(t) + sec(t) and y = tan(t) - sec(t), with the goal of eliminating the parameter t to derive expressions for x and y. The subject area involves trigonometric identities and calculus, particularly derivatives.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the equations by expressing x in terms of sine and cosine, but expresses uncertainty about how to proceed further. Other participants question the feasibility of eliminating the parameter and suggest exploring trigonometric identities.

Discussion Status

The discussion is ongoing, with participants sharing thoughts and expressing curiosity about the problem. Some guidance has been offered regarding the use of trigonometric identities, but no consensus or clear direction has emerged yet.

Contextual Notes

The original poster mentions a specific requirement to eliminate the parameter before taking the derivative, indicating a potential constraint in their approach. There is also a reference to needing additional trigonometric identities to aid in the process.

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x=tan(t)+sec(t) and y=tan(t)-sec(t)

I have to take the derivative, but it specifically states that I must eliminate the Parametric to do so (I think as a way to check we can do this...oops)

I was thinking that I could turn the x into:
x=sint+1/cost and then I could go from there, the only problem is that I have no idea where to go.

If anyone has any ideas that would help me get this into a trig identity so I can solve for t, I would love it!
 
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xy = ?
It's also helpful to know a few trig identities involving secant and tangent.
 


you can do that?
 


hmmm

good call. Thank you soooooooo much!
 

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