What is the equation for the tangent line in parametric equations?

In summary: But it is easy to check that the equation is still valid: just substitute t=0 or pi in the equation for the tangent.In summary, you can find the equation of the tangent line to a curve by finding the slope and substituting in the corresponding points.
  • #1
ziddy83
87
0
??Parametric equations??

hey what's up,
ok i have a question on differentiating parametric equations. The question says to find the equation of the two tangent lines to the curve. here's the equations...

[tex] x = 6 cos t [/tex]
[tex] y= 2sin2t[/tex]

Now, after i differentiate them, do i just plug in the corresponding point? , here's what i got after i differentiated them...

[tex] \frac {dy}{dx} = \frac {2cos2t} {(3)(-sint)} [/tex]

after plugging in the corresponding point for t, i will have the slope, but is that slope for both of the equations? :confused:
 
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  • #2
Your reasoning is quite correct except for the fact that you will get not a 3 in the denominator but a 6. Yes after you apply the chain rule, all you have to do is substitute t.
 
  • #3
He'll get a 3 since y'=4cos2t, x'=-6sint and 4/6=2/3.
 
  • #4
ziddy83 said:
hey what's up,
ok i have a question on differentiating parametric equations. The question says to find the equation of the two tangent lines to the curve. here's the equations...

[tex] x = 6 cos t [/tex]
[tex] y= 2sin2t[/tex]

Now, after i differentiate them, do i just plug in the corresponding point? , here's what i got after i differentiated them...

[tex] \frac {dy}{dx} = \frac {2cos2t} {(3)(-sint)} [/tex]

after plugging in the corresponding point for t, i will have the slope, but is that slope for both of the equations? :confused:


It is the slope of the tangent line of the CURVE.

ehild
 
  • #5
How do i find the corresponding points? lol...
 
  • #6
Hello

Now that you have the slope, you still need to write down the equation for the tangent:

y = slope*(x - 6cost) + 2sin2t​
I guess this will answer this question fully.

I made a drawing of the curve, a choosen point and its tangent, in MS Excel.
I attach it to this post, compressed in a zip file.
By changing the reference point, you can see that the equation for the tangent is ok: it touches the curve smoothly.
There is a small difficulty to t=0 or pi because the slope becomes infinite (the tangent is vertical then).
 
Last edited:

What are parametric equations?

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. These equations are used to describe a wide range of mathematical, physical, and scientific phenomena.

How are parametric equations different from standard equations?

The main difference between parametric equations and standard equations is that parametric equations use one or more parameters to define the relationship between variables, while standard equations use only the variables themselves.

What are the advantages of using parametric equations?

Parametric equations have several advantages over standard equations. They can provide a more concise and efficient way to describe complex relationships, they allow for greater flexibility in solving problems, and they can often provide more accurate solutions.

What are some common applications of parametric equations?

Parametric equations are used in a variety of fields, including physics, engineering, and computer graphics. They are commonly used to describe the motion of objects, the behavior of systems, and the shape of curves and surfaces.

What is the process for graphing parametric equations?

To graph parametric equations, first choose a range of values for the parameter and plug them into the equations to find corresponding values for the variables. Then plot these points on a graph and connect them to form a curve. The resulting graph will show the relationship between the variables and the parameter.

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