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Parametric equations with sine and cosine

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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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Опубликовано:

21 авг 2024

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Комментарии : 70

@Minskpotato Год назад

Video starts at 4:37

@nigit7451 5 лет назад

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

@Dr.Waffles 5 лет назад

@Tokisaki Kurumi lol

@wanyinleung912 5 лет назад

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

@hocineslamene9135 4 года назад

COBALT

@BigDBrian 5 лет назад

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 5 лет назад

4:36

@gordonchan4801 5 лет назад

F∆7 omit3 omit5

@jakekeene3527 3 года назад

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

@yurackjung9321 3 года назад

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

@SuperStruct 5 лет назад

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

@StellarShowtime Год назад

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

@jesussaquin6266 Год назад

That introduction should automatically be a subscription

@chaosredefined3834 5 лет назад

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 2 года назад

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 2 года назад

@@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.

@__-oq6nb 5 лет назад

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

@blackpenredpen 5 лет назад

Glad to hear l!

@yorkshire_tea_innit8097 2 года назад

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 5 лет назад

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

@alexkidy 5 лет назад

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

@protocol6 5 лет назад

lol.. I knew you were an Ood!

@holyshit922 5 лет назад

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)

@linnil 3 года назад

4:40 caught me off guard 😭😭

@goose5814 Год назад

You're the goat, love the videos!

@richardfredlund3802 3 года назад

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)

@iordachebeniamin6969 5 лет назад

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

@manthansunilhalarnkar 5 лет назад

Yeah, that infinity (graph) ♥

@mjz5853 5 лет назад

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

@purushotamgarg8453 5 лет назад

but sin(t) is negative when pi

@RodolfoAlvarez66 3 года назад

Thank you for the explanation.

@ThePianofreaky 5 лет назад

X=cos(t) Y=sin(πt)

@chameleman1870 2 года назад

Thank you

@ivanrubiomorales1818 4 года назад

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

@zza7195 5 лет назад

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))

@hashimamin1056 3 года назад

Great video thanks

@dmddjack 5 лет назад

wow nice bgm from jay chou XD

@blackpenredpen 5 лет назад

Thanks!!!

@MrRyanroberson1 5 лет назад

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

@benjaminkuo4669 3 года назад

legend

@mesimoke4872 Год назад

That was an ood thing to see ☺️

@rizkyagungshahputra215 5 лет назад

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=∞

@gordonchan4801 5 лет назад

where are the arrows for the bow tie?

@DruishQueen 4 года назад

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 4 года назад

and now that would be normal...

@alexkidy 5 лет назад

In Brazil we called parametric equations.

@lucasvilainmatras8338 5 лет назад

Ele falou no meio do vídeo :/

@NoNameAtAll2 5 лет назад

You called them what?

@ankurrai8677 5 лет назад

In India, we too.

@marcioamaral7511 5 лет назад

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

@marcioamaral7511 5 лет назад

Ankur Rai Actually it's universal

@PollyMwangi-cp3jn 5 месяцев назад

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

@mychevysparkevdidntcatchfi1489 5 лет назад

Lissajous was here!

@qijun1205 5 лет назад

曹老师✌

@guillaume6373 5 лет назад

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

@marcioamaral7511 5 лет назад

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 5 лет назад

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

@DjVortex-w 5 лет назад

I feel like we are running in circles here.

@stevenson720 5 лет назад

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.