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

In summary, the conversation is about finding the derivative of a parametric equation x=tan(t)+sec(t) and y=tan(t)-sec(t). The individual is looking to eliminate the parametric in order to solve for t and is seeking help to do so. They suggest turning x into a trig identity, but are unsure of the next steps. The conversation ends with someone offering to help and the original person expressing gratitude.
  • #1
BoldKnight399
79
0
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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  • #2


xy = ?
It's also helpful to know a few trig identities involving secant and tangent.
 
  • #3


you can do that?
 
  • #5


hmmm

good call. Thank you soooooooo much!
 

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

How do you eliminate parametric to derive x and y in tan(t)+sec(t) and tan(t)-sec(t)?

In order to eliminate parametric to derive x and y in tan(t)+sec(t) and tan(t)-sec(t), we can use the trigonometric identity, tan(t)=sin(t)/cos(t) and sec(t)=1/cos(t). By substituting these identities, we can rewrite the equations as x=sin(t)+1 and y=sin(t)-1.

What is the purpose of eliminating parametric in this equation?

The purpose of eliminating parametric is to express the equation in terms of x and y, making it easier to manipulate and solve for specific values of x and y.

Can you explain the steps involved in eliminating parametric?

The steps involved in eliminating parametric are: 1) Substitute the parametric equations with their corresponding trigonometric identities. 2) Rewrite the equations in terms of x and y. 3) Solve for x and y by using algebraic methods.

Are there any other methods to eliminate parametric in this equation?

Yes, there are other methods to eliminate parametric in this equation such as using inverse trigonometric functions or converting the parametric equations into polar coordinates.

How can eliminating parametric help in solving the equation?

Eliminating parametric helps in solving the equation by converting it into a form that is easier to manipulate and solve. This allows us to find specific values of x and y and graph the equation on the Cartesian plane.

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