Finding the equation for a tangent line (Parametric Equation)

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Homework Help Overview

The problem involves finding the equation of the tangent line to a curve defined by parametric equations, specifically at the point (1, sqrt(2)). The original poster seeks the tangent line in the form y=f(x) without using the parameter.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find the slope of the tangent line using derivatives derived from the parametric equations. Participants discuss the calculation of the slope and the subsequent use of the point-slope form of the line.

Discussion Status

Participants are actively discussing the calculations involved in determining the slope and the tangent line equation. There is some confusion regarding the correctness of the derived equation, with multiple participants questioning the accuracy of the numerical values used in their calculations.

Contextual Notes

There is a mention of using a specific notation for the parameter (θ instead of ∅), and participants are exploring the implications of using decimal approximations versus exact values in their final equations.

PsychonautQQ
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Homework Statement


Find an equation of the tangent to the curve given by
x=tan(∅)
y=sec(∅)
at the point (1,sqrt(2))

The answer should be in the form y=f(x) without ∅


The Attempt at a Solution


Tangent line equation...
y-y*=m(x-x*)
m = dy/dx
m = sec(∅)tan(∅) / (sec^2(∅)
m = tan∅ / sec(∅)
m = sin∅

This is what I did so far, I'm a bit lost obviously
 
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Hint: use "θ" for theta, not "∅".

Find out what θ is when x = 1 and y = sqrt(2) (this is from the given point). Plug the value for θ in your expression for dy/dx to get your slope.
 
Okay, so i did that and end up with m = sqrt(2)/2.
If i use the equation
y-y*=m(x-x*)
with
y* = sqrt(2)
x* = 1 and solve it i get
y=(sqrt(2)/2)x+2.1
but i type this into my online course and it says it's wrong?
 
PsychonautQQ said:
y=(sqrt(2)/2)x+2.1
I'm not getting 2.1.
 
When i type in
y=.71x+.71 it gives me the wrong answer as well. ;-(
 
Maybe it is because you are using a decimal approximation? I'm pretty sure the exact form of the last equation you wrote is correct.
 

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