Maclaurin series of sin(x) | Series | AP Calculus BC | Khan Academy

Approximating sin(x) with a Maclaurin series (which is like a Taylor polynomial centered at x=0 with infinitely many terms). It turns out that this series is exactly the same as the function itself! Created by Sal Khan.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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[Pancake]

"yeah... zero would be an even number" LOL i love sal khan so much

[mulimotola]

5:32 lol that was great, it's like he has multiple threads running in his brain

[_sona_malhotra]

He didn't state about the conditions of Maclaurin's expansion being satisfied, basically when f possesses derivatives in R of every order and that R_n (remainder) tends to zero as n tends to infinity.

[QuietQuakePro]

The calc AP is tomorrow, thanks so much for helping me understand Mclaurin!

[azizharnadez]

expand the function f(x)=sinx about the point x=pie/3, using taylors expansion, and evaluate sin 75

[BitterHugOfMortality]

I know this is nitpicky, but at 2:43 when he's talking about the limit of the Taylor series, he says "If you go to infinity, you're going to be pretty much at cosine of x." This is actually a mischaracterization of limits. If you calculate the Taylor series to infinity, you will be exactly at cosine of x. That's how limits work. While this distinction is not necessarily a big deal for the purposes of understanding the mechanics of calculus, it is important for a deep understanding of the math. For example, the same is true of .999... equaling 1. If you tell them that .999 repeating "pretty much" equals 1, they won't understand the math. 999 repeating actually equals 1. It's the same exact number. Mischaracterizing limits as approximations doesn't help students understand these deeper relationships between numbers.

[Krabby_Patty]

Why couldnt Sal cover this six months ago when it was in my curriculum, I do not know, my hard luck I guess. But it will definitely help does who do have it in their subject matter in future.

[owenguo]

Not sure how it is going to help with solving the in
definite integral of ln(sinx)dx

[fsr]

Is there is simple way to take these two infinite series we have derived and create another Maclaurin series for Tan(x)?

Thank you

[dineshjangid]

Solution of e to the power asin inverse x Maclaren series

[_slvya]

Someone please explain why we need this

[sadafnaeem]

Sir can you plzz help me how can I find maclaurin series of sin36

[noahsrc]

how would i calculate sin(3) (with this), for example?

[_slvya]

Should the value of x be in radians or degree or could it be either ?

[horsethif]

Is the Infinite Series exactly == sin(x) or is it still an approximation? (at infinity)

[stormcorrosion]

@vickiormindyb You're just not a mathy person, I guess.