Precalculus teacher vs WolframAlpha student

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0:00 cos(cos^-1(pi))=?
1:20 Using Euler's formula to get complex cos(z)
2:47 Getting an expression for complex cos^-1(w)
6:02 A complex value for cos^-1(π)
6:35 Getting cos(cos^-1(π))=π
10:32 check out Brilliant

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[Wyattporter]

I love how threatening this is. “You want to go the complex world? I will take you there.”

[intheshellify]

I "challenge the teacher all the time" cause they are human too.
Hold up, nobody said anything about putting it on the test. I was just playing. You the man. All hail the teacher and his very sufficient answers!!!!

[XenOzrxT_]

This dude just pulled an “I will show you the world” song from Aladdin by taking us to the complex world lol.

[daniellind]

I know it’s just his microphone but there’s something so wholesome about him holding a plush pokeball while talking

[militantpacifist]

Imagine you’re in high school or college barely learning this and all of the sudden in the exam there’s a problem that says “Prove that Cos(Cos−^1(π)) = π.”

[AmritGrewal]

Wolfram alpha is weak AF, we need wolfram sigma

[bobfish]

Just realized how god tier he is at the color swapping

[thalajmalhotra]

The satisfaction on his face after cancelling in the last step is just incredible

[marcushendriksen]

Holy shit, bprp is really leaning into the Confucius look these days

[iamstickfigure]

I love this video. Because when I saw the cancel with caution video, I had a suspicion that complex numbers might fix the problem. It's great to see it all laid out like that.

[Mrjcowman]

This is awesome. Everyone tends to react to complex numbers with the sentiment that "they make math more confusing" but this problem is an excellent example of how complex numbers can actually make math more sensible.

[SgFlaxy]

Your marker technique is really impressive!

[andreasibilla]

i finished this video and my reaction was "...wow"

[biggerdoofus]

Wait, but what if the student gives the complex definition of cosine, but then stops there? The complex definition already shows that pi is in its range, so as long as Euler's contribution is true and the function arccosine is defined as the inverse operation of cosine, then by the definition of arccosine the solution would be correct.

[gilber]

Here’s what I’d say. The purpose of precalc is understand how functions work. Cosine’s range by all sense of it’s definition w.r.t to the unit circle (in the real xy plane) does not include pi. So for the purpose of precalc, the teacher is correct and the student was being a prick. However if I was a teacher, put that on a hw/quiz/test, and the student somehow did the complex analysis correctly, I’d give them the credit

[risheraghavendira]

true mathematician's happiness @9:45
feels so good

[SimonPetrikovv]

The beauty of it is that any of the solutions to z = cos^-1(pi) that you've found will indeed give us cos(cos^-1(pi)) = pi, since things will cancel out on the denominator/numerator and because we have e^(2i*pi*n) = 1

I call this art

[lorigulfnoldor]

I just love Euler's formula. It's so powerful! It lets you save on you memory so you don't have to remember all those trig laws, since they can be so easily derived from it!

[ChronosWS]

It is always insufficient for the student to recite the answer if they do not understand why it is the answer.

[aMartianSpy]

cosine is even, odd in the complex world

or maybe its odd, even in the complex world

i odd to know