Parametric equations with sine and cosine

We will go over 5 examples of parametric equations with sine and cosine. We will see how to convert parametric equations to rectangular (aka Cartesian). And we will also graph these parametric equations.
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[@Minskpotato]

Video starts at 4:37

[@jakekeene3527]

Nice way to wake up, you scared the shit out of me lol.

[@nigit7451]

Cosine ---------- =co Sine

[@Dr.Waffles]

@Tokisaki Kurumi lol

[@wanyinleung912]

sinx ------- n =six =6

[@hocineslamene9135]

COBALT

[@BigDBrian]

the loss of generality comes from the fact that sin(t) can be negative, but in the triangle you used to figure out its length, it can only be positive. I think that's worth stating.

[@Eatmyorigami]

4:36

[@gordonchan4801]

F∆7 omit3 omit5

[@protocol6]

lol.. I knew you were an Ood!

[@alexkidy]

Nice. I had some difficulty to understand the last one.The others are easy. Tks!

[@yorkshire_tea_innit8097]

What do you do when cos and sin are both on the same equation. e.g. x=(sin(t)*a)+cos(t) y=(sin(t)*a)+sin(t)

[@neilgerace355]

The logo of the Australian Broadcasting Corporation is based on a Lissajous curve: x = cos t; y = sin 3t

[@yurackjung9321]

This is so much better than my analysis teacher just giving us a ws to figure it out on our own... thanks

[@SuperStruct]

I've been waiting for this video for so long and I just realized it now, been thinking about an Ood reference for so long

[@__-oq6nb]

Yes! Just in time! We just started going over em!!! Thank you!

[@blackpenredpen]

Glad to hear l!

[@chaosredefined3834]

x = cos(t), y = sin(2t) = 2sin(t)cos(t) = 2sin(t)*x x = cos(t), y/2x = sin(t) x^2 + y^2/(4x^2) = 1 4x^4 - 4x^2 + y^2 = 0

[@ishqaqamar2789]

Can't believe you just saved me from developing a headache over not being able to solve a similar problem with a comment from three years ago.

[@chaosredefined3834]

@@ishqaqamar2789 You're welcome. I did do two steps at once. I probably should have a second last line of 4x^4 + y^2 = 4x^2, after which I subtract the 4x^2 from both sides, giving the final line.

[@StellarShowtime]

Thanks for helping with a shortcut way of converting parametric equations to rectangular via trig sub!

[@linnil]

4:40 caught me off guard 😭😭

[@jesussaquin6266]

That introduction should automatically be a subscription

[@iordachebeniamin6969]

i belive something change at 4:41 but i forgot.I have a feeling i saw something odd

[@holyshit922]

This parametrization can be rationalized , see how can we derive Euler's substitution (Cut the curve y^2=ax^2+bx+c with secant line or Draw bisector of angle complementary to theta in our trig substitution picture to get another right triangle In this new triangle choose angle Pi/4+theta/2 and calculate its tangent)

[@richardfredlund3802]

so if you had x=cos t and y =sin 3t would you have a triple loop and so on? ... i haven't checked this but it seems logical. (edit: I see from other comments the answer for 3t case is yes and it is Lissajous curve)

[@manthansunilhalarnkar]

Yeah, that infinity (graph) ♥

[@RodolfoAlvarez66]

Thank you for the explanation.

[@mjz5853]

sin(t) = ±sqrt(1-x^2), because sin(t) is not necessary non-negative when 0

[@purushotamgarg8453]

but sin(t) is negative when pi

[@dmddjack]

wow nice bgm from jay chou XD

[@blackpenredpen]

Thanks!!!

[@chameleman1870]

Thank you

[@hashimamin1056]

Great video thanks

[@goose5814]

You're the goat, love the videos!

[@DruishQueen]

Okay here is the deal: wear the mask to class. Just give the lecture like always, and be like "what, what are you guys looking at" like totally serious and normal. And as always, that's it.

[@calebschrock4653]

and now that would be normal...

[@PollyMwangi-cp3jn]

Do y=cos2t, x= sin t. Someone help please

[@MrRyanroberson1]

I made a function in desmos that allows for the rotation in 3-space of 3-up-projections of that last function, so all I can think of are saddles, not bow ties XD

[@ivanrubiomorales1818]

x=4cos^2(t) and y=2sin^2(t)

[@gordonchan4801]

where are the arrows for the bow tie?

[@ThePianofreaky]

X=cos(t) Y=sin(πt)

[@zza7195]

We can make an easy theorem to be faster : let x and y be such that: x=φ(t), where φ is a bijection y=ψ(t) then φ⁻¹(x)=t so y=ψ(φ⁻¹(x))

[@NorlineParker]

I'm cackling at the Ood 😭

[@rizkyagungshahputra215]

lim x goes to ∞ cotan(x^(1/lnx))? i got cotan(e) but when i checked the answer in wolfram, it turned out that there is no limit because there is infinitely many singularity in every neighborhood about x=∞

[@benjaminkuo4669]

legend

[@alexkidy]

In Brazil we called parametric equations.

[@lucasvilainmatras8338]

Ele falou no meio do vídeo :/

[@NoNameAtAll2]

You called them what?

[@ankurrai8677]

In India, we too.

[@marcioamaral7511]

Alexandre César Existem muitas equações paramétricas dentro da matemática Essas aí são apenas algumas

[@marcioamaral7511]

Ankur Rai Actually it's universal

[@mesimoke4872]

That was an ood thing to see ☺️

[@stevenson720]

Hi, id be interested in how e^iz = cos z . I'm struggling to find good examples of people flicking back and forth between complex and trig and it seems useful for differential equations. Thank you. Any one with any good links I'm all ears please.

[@guillaume6373]

integral of 1/(1+x^2) next please :)

[@marcioamaral7511]

Swagger Lemon There's not even the need to do any subs The anti-derivative of 1/(1+x^2) is arctan(x) + C or -arcctg(x) + C

[@marcioamaral7511]

Swagger Lemon If that's the case then it's fine to use one He can use a trig as you suggested or an hyperbolic one He can even do partial fractions Many possibilities

[@qijun1205]

曹老师✌

[@mychevysparkevdidntcatchfi1489]

Lissajous was here!

[@MrQwefty]

Happy halloween! XD

[@DjVortex-w]

I feel like we are running in circles here.

[@romanqc]

Hello

[@danielfernandocarballo1890]

Odd

[@porterchien4782]

明明就不喜歡牽手～

[@lucasfrykman5889]

spooky

[@spockfan2000]

:D

[@ZyloSol99]

:D

[@edgbaston149]

Thank you