Tangent Line on a Parametric Curve

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Homework Help Overview

The problem involves finding the equation of the tangent line to a parametric curve defined by the equations x=sin(3t) and y=cos(3t) for the parameter range 0≤ t ≤ 2pi, specifically at the point where t=2pi/9.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need for a derivative to find the tangent line equation and question what specific information is necessary for this calculation. There is mention of a derivative that has been computed, but uncertainty remains about the next steps and how to evaluate it at the specified parameter value.

Discussion Status

The discussion is ongoing, with participants exploring the necessary components to find the tangent line. Some have provided partial calculations, while others are seeking clarification on how to proceed from the derivative to the tangent line equation.

Contextual Notes

There is a lack of explicit consensus on the method to find the tangent line, and participants are navigating through the requirements of the problem without a complete resolution.

suchgreatheig
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Homework Statement


A curve is defined parametrically by x=sin3t, y=cos3t, 0≤ t ≤ 2pi. Find the equation of the line tangent to the curve at the point defined by t=2pi/9.


Homework Equations





The Attempt at a Solution


?
 
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suchgreatheig said:

The Attempt at a Solution


?

Since you need to find the equation of a tangent, what do you need to find this equation?
 
I know that I need a derivative which I got as -3sinst/3cos3t, but I'm stuck from there.
 
suchgreatheig said:
I know that I need a derivative which I got as -3sinst/3cos3t, but I'm stuck from there.

so if dy/dx=-sin(3t)/cos(3t), what is the gradient when t=2π/9 ?
 

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