Tangent Lines of Parametric Curves

This calculus 2 video tutorial explains how to find the tangent line equation of parametric functions in point slope form and slope intercept form.

Derivatives of Parametric Functions:

Tangent Lines of Parametric Curves:

2nd Derivative - Parametric Equations:

3rd Derivative of Parametric Curves:

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Horizontal & Vertical Tangent Lines:

Area of Parametric Curves:

Arc Length of Parametric Curves:

Surface Area of Parametric Curves:

Polar Coordinates - Introduction:

Tangent Line Equations - Polar Form:

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Horizontal & Vertical Tangents - Polar:

Area of Polar Curves:

Area Between Polar Curves:

Arc Length of Polar Curves:

Surface Area of Polar Curves:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[dominictumulty]

You ARE my professor for ALL my classes.

[NickMirambeau]

I hope you know you're *actually* a legend. That is all.

[willsennett]

Exam in 8 hours. This helped a lot. Thanks for doing this for as long as you have been.

[-a]

Thanks you taught me how to do it with one example :)

[AK-olrm]

Am one of the students in Alexandria university in Egypt facult of engineering
Thank you dr
Your vedios so helped me🙏🙏🙏

[georgesadler]

Professor Organic Chemistry Tutor, thank you for an incredible video/lecture on Tangent Lines of Parametric Curves in Calculus Two. Parametric Curves and Surfaces are a huge part of Differential Geometry. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[MotsekiMosia-ex]

NO WORDS CAN DESCRIBE HOW THANKFUL I AM, I JUST WANT TO SAY THANK YOU SO MUCH FOR BEING THERE FOR ME AND OTHERS

[Chikulamayembe]

The man is a genius. Keep you the good work Sir.

[bensmith]

This helped a lot and was super simple to follow along with

[rimjhim]

Thank you so much for making my calculas lessons easier!! My exams are around and I can't explain my gratitude right now !!

[alejandrachavarria]

This was so helpful thank you so much! I feel ready for my exam now!

[butchmikey]

stressing over my ap exam. your a real help 🙏

[hannahhyland]

watching this before my calculus 3 exam. this account is the reason i’m doing well

[MineWiz]

My professor just put up the most crappy lecture ever for this section. Thank you for the help!

[clarencehung]

Hi, i have a question. i came accross a qeustion where it states "find the equation of tangent when t = 0 ". which makes the point xy(0, 0) and alos the slope 0. Does that mean i need a different appproach? or does that mean the equation does not exist?

[roniebedrijo]

How to find the minimum L of the Ladder in Metters

[athenadominguezcastillo]

So, how would you do this by eliminating the parameter?

[aimanimtiaz]

sir can anything be said about the tangents to the curves y=sinmx and y=sin(x/m)at the origin (ma constant not equal 0)give reason

[quosswimblik]

Here's a type of parametric curve I found I call triangle curves. heres the mathematica code.
Manipulate[
ListPlot[Table[
If[t > d, {(e + 1) Cos[t], (e + 1) Sin[
t]}, {(e + 1 - c (t/(d))) Cos[t], (e + 1 - c (t/(d))) Sin[
t]}], {t, 0, Pi, 0.011}]], {c, 0, e + 1}, {d, 0.011, Pi}, {e,
0, 4}]

[crazypyrokitty]

Ohmigoodness that answer on the last one is so much quicker if you wait until the end to put in your pi/3- so get (-3/4cotO) then put in your pi/3 for O (theta).